Unit+3

toc =**Lab: Simple Harmonic Motion**= Objective: What is the relationship between the force that a spring exerts on a mass and the distance the spring stretches? Hypothesis: the Further the spring stretches the more force the spring will exert on the mass. Procedure: We are given a stand with a spring on it We will attach different weights and see when the object stops moving the weight when the spring is not moving is the same as the force the spring is exerting on the object It must be at rest. We will measure how far the spring is stretched and then will be able to relate the force and distance stretched. We will then graph the distance against the force exerted to find a trend that relates the distance a spring stretches to the amount of force it exerts.

Data:

Graph:
 * Mass(kg) || Force (newtons) || Distance streached (m) ||
 * 0.005 || 0.049 || 0.013 ||
 * 0.010 || 0.098 || 0.028 ||
 * 0.015 || 0.147 || 0.045 ||
 * 0.020 || 0.196 || 0.060 ||
 * 0.025 || 0.245 || 0.075 ||
 * 0.030 || 0.294 || 0.090 ||
 * 0.035 || 0.343 || 0.106 ||
 * 0.040 || 0.392 || 0.125 ||
 * Mass(kg) || Force (newtons) || Distance Streached (m) ||
 * 0.100 || 0.98 || 0.013 ||
 * 0.200 || 1.96 || 0.024 ||
 * 0.300 || 2.94 || 0.032 ||
 * 0.400 || 3.92 || 0.042 ||
 * 0.500 || 4.9 || 0.053 ||
 * 0.600 || 5.88 || 0.066 ||
 * 0.700 || 6.86 || 0.076 ||
 * 0.800 || 7.84 || 0.087 ||
 * 0.800 || 7.84 || 0.087 ||

'



Analysis: The r^2 value is equal to the spring force constant. The data shows that the relationship between the springs stretch and the force it exerts is a direct linear relationship. As more weight was added the spring stretched more and placed more force on the mass. The lab also showed that Hooke's law is correct and the spring force can be found by multiplying the spring force constant and the distance stretched. In the equations fpor the line: y = 97.76x and y = 3.0895x, y is equal to the spring force and the slope is the spring force constant. the error from the lab was hum,an error due to problems in measurement and keeping the spring at rest. Part b: objective: What is the relationship between the period of oscillation and the mass? Hypothesis: as the mass increases so will the period of oscillation because of he increase of inertia. Analysis: In this section my hypothesis was correct as the relationship between period of oscillation and mass is directly square root proportional. T = 2pi / sqrt(k) * sqrt(m) therefore slope represents 2pi / sqrt(k) and x represents mass. The coefficient for the slope is equal to 3.09 for our equation but should be around 3.5 this is due to human error in timing and counting the number of oscillations.
 * Mass (g) || Period ave (s) ||  ||   ||
 * 25 || .61 ||  ||   ||
 * 35 || .721 ||  ||   ||
 * 45 || .797 ||  ||   ||
 * 55 || .862 ||  ||   ||

=Lab Slinky:=

** Investigate: Waves on a Spring **

The class needs to make a “stadium wave”. Do it. To find the relationship between wave speed and frequency. To find the relationship between wave speed and wavelength. To distinguish between transverse and longitudinal waves.
 * Prelab:**
 * 1) How should you move as an individual to participate? One should stand up as the person next to them sits down.
 * 2) How should the class move as a unit? The movement should flow and be connected to the person next to them.
 * 1) What represents the motion of the wave? The passing of movement from one person to the next.
 * 2) What represents the motion of the energy? The standing up represents the energy in motion as it passes.
 * 3) What variables can be changed in your “stadium wave”? who starts the wave and the speed at which it travels.
 * Objective:**


 * Hypotheses:** wave speed is directly related to both frequency and lambda. As the lambda or frequency increase so does the wave speed.


 * Materials:** slinky and snake spring, timer, tape, meter stick


 * Procedure:**
 * //Part I// – Marking the floor**
 * 1) Place strips of masking tape approximately .75m long on the floor at 0.0 m, 5.0 m and 10.0 m.
 * 2) **//Mark//** and **//label//** a heavy ink/pencil line in the **//center//** of the tape at 0m.
 * 3) Mark and label lines 10.0 cm, 20.0 cm and 30.0 cm to the **//left//** and **//right//** of your center mark on each.


 * //Part II// – Making a transverse pulse**
 * 1) Stretch your spring between the 0.0 m and 5.0 m tape marks on the floor with the rope loops around your wrist being located about 0.5 m beyond the tape marks on the floor.
 * 2) Move your hand back and forth at right angles to the stretched spring until you can produce a pulse that travels down only one side of the spring (that is, the bump on the spring due to the pulse is only on the right or left side of the spring).
 * 3) Send a pulse down the spring that has an **amplitude** of **10.0 cm**. Have the third member of your group time the pulse as it travels from 0.0 m to 5.0 m.
 * 4) Repeat steps #8-11 for pulses having amplitudes of 20.0 cm and 30.0 cm.
 * 5) Repeat steps # 8-11 for 10-m distance.


 * **// Table 1 - Speed of pulses (Spring A) //** ||
 * |||||| ** 5.0 meter total distance ** |||||| ** 10.0 meter total distance ** ||
 * **Amplitude (cm)** || **//10.0//** || **//20.0//** || **//30.0//** || **//10.0//** || **//20.0//** || **//30.0//** ||
 * **Trial 1 time (s)** || 0.59 || 0.44 || 0.39 || 0.41 || 0.45 || 0.31 ||
 * **Trial 2 time (s)** || 0.6 || 0.53 || 0.35 || 0.31 || 0.43 || 0.35 ||
 * **Trial 3 time (s)** || 0.6 || 0.52 || 0.35 || 0.32 || 0.49 || 0.33 ||
 * **Avg.time (s)** || .596 || .4967 || .3633 || .3466 || .4566 || .33 ||
 * **Distance (m)** || **//5.0//** || **//5.0//** || **//5.0//** || **//10.0//** || **//10.0//** || **//10.0//** ||
 * **Avg. Speed (m/s)** || 8.389 || 10.066 || 13.762 || 28.85 || 21.90 || 30.303 ||

ave speed = distance/ave time The speed of the waves is about the same for the three amplitudes because the distance is the same.
 * 1) Repeat steps # 8-11 for a more tightly coiled spring.
 * **// Table 2 - Speed of pulses (Spring B) //** ||
 * |||||| ** 5.0 meter total distance ** |||||| ** 10.0 meter total distance ** ||
 * **Amplitude (cm)** || **//20.0//** || **//30.0//** || **//40.0//** || **//20.0//** || **//30.0//** || **//40.0//** ||
 * **Trial 1 time (s)** || 1.11 || 0.91 || 0.88 || 1.04 || 1 || 1.02 ||
 * **Trial 2 time (s)** || 1.127 || 0.89 || 0.87 || 1.03 || 0.95 || 1.01 ||
 * **Trial 3 time (s)** || 0.977 || 0.94 || 0.76 || 1.02 || 1 || 0.99 ||
 * **Avg.time (s)** || 1.068 || .9133 || .8367 || 1.03 || .9833 || 1.006 ||
 * **Distance (m)** || **//5.0//** || **//5.0//** || **//5.0//** || **//10.0//** || **//10.0//** || **//10.0//** ||
 * **Avg. Speed (m/s)** || 4.6 || 5.47 || 5.97 || 9.71 || 10.17 || 9.94 ||
 * //Part III// – Making a longitudinal pulse**
 * 1) Make sure that the rope loops at the end of the springs are around your wrist. With your free hand, grasp the stretched spring about a meter from one end. Pull the meter of spring together toward yourself and then release it, being careful not to let go of the fixed end with your other hand! Another way to do this is to push the spring towards your lab partner and quickly bring it back to your original position.
 * Discussion Questions**
 * 1) How do the speeds of the waves compare for the 3 different amplitudes of the 5.0 meter distance?

the amplitude sis not influence the speed of the waves.
 * 1) Did amplitude influence the speed of the waves for the 5.0 meter distance?

these too were very similar to each other and show that the amplitude does not have a huge affect on the speed.
 * 1) How do the speeds of the waves compare for the 3 different amplitudes of the 10.0 meter distance?


 * 1) Did amplitude influence the speed of the waves for the 10.0 meter distance?

No it did not the only change in speed was due to distance based on the medium the wave was on.


 * 1) How do the speeds of the waves compare for the 5.0 meter and 10.0 meter distances?

The speed of the waves of the 10 meter was about twice that of the 5 meter.


 * 1) What changed when you measured the time for 10-m vs. the 5.0-m distance? Choose as many as apply.
 * 2) The medium changed.
 * 3) The wavelength changed.
 * 4) The speed changed.
 * 5) The frequency changed.

the slinky passed the waves at a much slower speed because the rings were further apart.
 * 1) How do the speeds of the waves compare for the 2 different types of springs?

longitudinal waves move parallel to the direction of motion while transverse waves move perpendicular to it.
 * 1) What are some differences between the longitudinal and the transverse wave?

Hw: Waves
a: Vibrations- are caused by forces that break the resting position of a vibrating object. A bobble head,when pushed will move from equilibrium to its max point at the right and to its max point to its left. every time the head passes equilibrium restoring forces work to slow down the movement and eventually stop the vibrations. b c: Periodic motion: a motion that is regular and repeating is referred to as a periodic motion. If a mass on a spring were to mark a paper as it was pulled constantly passes, the moving mass would form a sinusoidal graph. This is because the moving mass is a repeating and periodic motion. The vertical distance from equilibrium to a crest is amplitude. Period is the time for one complete cycle. Speed of a wave is d/t or wavelength/period, Frequency is how many waves o cycles pass in 1 second, reciprocal of period. Pendulum motion also makes a a sin graph. KE increases as the pendulum heads towards equal and decreases ac it heads away. D: A mass on a spring will have a similar graph because it is also a periodic motion that passes through equilibrium multiple times. Peroid of a spring can be represented by T=2n*(m/k)^.5. waves A B: nature of waves: Waves are a part of light, sound and motion. 2 different types, Mechanical Waves and Electromagnetic. Mechanical Waves require a medium to travel in, Electromagnetic do not require a medium. Medium is a material that carries a wave made of interacting particles. waves start from a disturbance that sends vibrations as a pulse moves through a medium. The repeating and periodic disturbance that moves through a medium from one location to another is referred to as a wave. in a wave one particle passes its energy to the next particle and so on creating a chain reaction. because of this waves transport energy not matter. C: Categories of waves: Transverse waves or Longitudinal (compression) waves. Transverse waves are ones in which the particles oscillate perpendicular to the direction of the wave travel. Longitudinal waves: mediums/particles oscillate parallel to the direction of wave travel. In longitudinal waves there's a region of compression which is high pressure and particles are closer together. There is also rarefaction It means that it is a less dense with low pressure particles are spread out more than usual. Transverse waves have a crest, the max displacement and a trough, the minimum displacement. Properties of waves:



http://www.cartoonstock.com/newscartoons/cartoonists/iba/lowres/iban275l.jpg =Lab Waves and frequency:= To determine the relationship between the number of harmonics, the frequency of the source, and the wavelength of transverse waves traveling in a stretched string.
 * Purpose: **

Hyothesis: as the frequency increases the number of antinodes will also increase. As the frequency increases the lambda decreases.

Electrically driven oscillator; pulley & table clamp assembly; weight holder & selection of slotted masses; black Dacron string;
 *  Materials: **


 * Procedure: **
 * 1) Set the frequency of the oscillator to zero. Set the amplitude to maximum.


 * 1) Measure the length L of the string.


 * 1) Dial up the frequency a little at a time until you acquire a standing wave. If you are careful, you should be able to get the fundamental. However, if you don’t, it’s okay… just record the correct number of antinodes along with the frequency.


 * 1) Measure the wavelength.

Data:
 * 1) Repeat for at least 7 different harmonics. These do not have to be consecutive.


 * **n ** || **//f //****(Hz) ** || **Measured **** l **** (m) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Calculated v (m/s) ** ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">11.6 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">14.38 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">166.81 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">23.3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">7.19 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">167.53 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">34.9 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">4.79 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">167.17 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">4 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">48 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">172.56 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">59.1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2.876 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">169.97 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">15 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">177.2 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">0.958 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">169.76 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">7 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">82.2 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2.054 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">168.84 ||

Analysis: In this lab the class tested the effects of different frequencies on a spring. the data proved that there is a direct linear relationship between frequency and the number of nodes and there is an inverse relationship between frequency and wavelength. I also learned that the relationship between tension and frequency is a direct square relationship. By using f = v / 2L, we could determine the velocity of wave in string, which was 169.76 m/s. The velocity value should be constant in the data table 1 because the v = square root( tention / linear density), and the tension of the medium in the experiment didn't change at all. Also in data chart 2, which proved the inverse relationship of frequency and wavelength, provided the similar velocity as data chart 1. Due to f = y = v / wavelength, v is equal to the A value in y = Ax ^ -1, which was 170. 59. It was similar to the velocity value i calculated in data chart 1. the source of human error was not being able to see the exact largest anti-nodes and the harmonic frequencies were limited.
 * **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Mass Hanging (kg) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Tension in the string (N) ** || **//<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">f //****<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">(Hz) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Measured **** l ****<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;"> (m) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Calculated v (m/s) ** ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">0.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">4.9 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">34.1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">122.59 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">9.8 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">47.7 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">171.482 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">1.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">14.7 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">57.7 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">207.432 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">19.6 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">65.3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">234.754 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">24.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">73.9 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">265.671 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">29.4 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">81 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">291.195 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">34.3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">88.1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">316.72 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">34.3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">88.1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">316.72 ||  ||
 * Calculate the speed of the wave for each harmonic. (SHOW A SAMPLE CALC!)
 * v = f * wavelength. therefore v = 11.7 * 14.38 = 168.246m/s
 * Calculate the tension in the string. (SHOW A SAMPLE CALC!)
 * F = m * g . F = 0.5 * 9.8 = 4.9N

1. What is the name given to a point on a vibrating string at which the displacement is always zero? The point on a vibrating string where the displacement is zero is called the node.

2. What is the name given to a point at which the displacement is always a maximum? Displacement is at a maximum at the anti nodes

3.How is the length of the string related to the wavelength for standing waves? the most the wavelength can be is twice the length of the string.

4.What is the longest possible wavelength for a standing wave in terms of the string length? the longest possible wavelength is twice the string length.

5. Use your graph to find the frequency for n = 20. (Try it. Does it work?) 236.1 Hz

6. What is the relationship between the speed of the wave and the harmonic number? There is no relation.

7. What is the relationship between the speed of the wave and the frequency? there is a direct relationship between the speed of the wave and its frequency.

8. What is the relationship between the wavelength and the harmonic number? there is an inverse relationship between the wavelength and the harmonic number.

9.What is the relationship between the wavelength and the frequency? There is an inverse square relationship between wavelength and frequency.

Hw: Waves and Sound:
a traveling wave is a wave that travels through a medium and interacts with other waves. Traveling waves are observed when a wave is not confined to a given space along the medium. The most commonly observed traveling wave is an ocean wave. There are other points along the medium whose displacement changes over time, but in a regular manner. These points vibrate back and forth from a positive displacement to a negative displacement; the vibrations occur at regular time intervals such that the motion of the medium is regular and repeating. A pattern is readily observable. nodes are the places between waves that are the smallest and separate crests. when two waves pass together they add and form a third wavelength that is greater than both. If they are inversely moving then they will make a frequency in the middle.

Sound waves and music: Sound wave is a mechanical wave that is carried on a medium which is usually air but can also be other materials like water or steel. Sound waves in air are longitudinal. sound is perceived by changes between low and high pressure in ones ear. Frequency: is how often the particles of the medium vibrate when a wave passes through the medium. The frequency wave is measured as the number of complete back-and-forth vibrations of a particle of the medium per unit of time. 1 hertz= 1 vibration/second. waves can interfere with one another and cause disruptions(cancelling out) or constructions(joining). The Doppler effect: the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for the observer and the source are approaching and an apparent downward shift in frequency when the observer and the source is receding.

[] =Lab: Resonance tubes:=
 * Objective: ** What is the relationship between the length of a tube and its resonant frequencies?


 * Hypothesis:** the longer the tube the higher the resonance frequencies will be.


 * Materials: ** Resonance tubes with length scale marked on the tube, audio generator, speaker, class thermometer.

1) Measure the room temperature of the air and record it in Data Table 1. If the thermometer in the room measures temperature in oF it is necessary to convert to oC.
 * Experimental Procedure: **
 * // Part A: Closed Tube //**

2) Your teacher will assign you a frequency, between 300 and 800 Hz. Calculate the wavelength of this sound, using the speed from Step 1.

3) Calculate the theoretical length of the column of air in the closed tube of the first 5 harmonics. Circle the ones between 0 and 2.6 meters.

4) Set the audio generator to emit the frequency that has been assigned to you. Lower the volume (amplitude) so that it is just barely audible.

5) Set the speaker next to the open end of the resonance tube. Set the tube to the first calculated length. Adjust the length of the tube by moving the inner tube in small increments in or out, until you hear the sound at its maximum amplification. Record the adjusted lengths as the Measured.

6) Repeat the procedure for the other calculated lengths.

Table A: Closed Tube
 * ** Frequency (Hz) ** || ** Harmonic Number ** || ** Length of tube – Calculated (Theoretical) ** || ** Length of tube – Calculated (Expeimental) ** || ** % Error ** || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">absolute difference m || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">length width end affect correction m || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">% error ||
 * ^  ||^   || ** (m) ** || ** (m) ** ||^   ||   ||   ||   ||
 * 650 || 1 || 0.13375 || 0.067 || 49.9065421 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.06675 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.07735 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">13.38074 ||
 * 650 || 3 || 0.40125 || 0.3395 || 15.3894081 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.06175 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.34485 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">1.551399 ||
 * 650 || 5 || 0.66875 || 0.601 || 10.1308411 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.06775 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.61235 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">1.853515 ||
 * 650 || 7 || 0.93625 || 0.852 || 8.99866489 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.08425 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.87985 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">3.165312 ||
 * 650 || 9 || 1.20375 || 1.23 || -2.18068536 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">-0.02625 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">1.14735 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">-7.20356 ||
 * 650 || 11 || 1.47125 || 1.426 || 3.07561597 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.04525 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">1.41485 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">-0.78807 ||


 * // Part B: Open Tube //**

7) Your teacher will assign you a frequency, between 300 and 800 Hz. Calculate the wavelength of this sound, using the speed from Step 1.

8) Calculate the theoretical length of the column of air in the open tube of the first 5 harmonics. Circle the ones between 1.3 and 2.6 meters. These are the harmonics that you will try to hear experimentally. NOTE: You cannot test lengths SMALLER than 1.3 m or BIGGER than 2.6 m. Caluclate bigger harmonics to substitute for those values less than 1.3 m.

9) Set the audio generator to emit the frequency that has been assigned to you. Lower the volume (amplitude) so that it is just barely audible.

10) Set the speaker next to the open end of the resonance tube. Set the tube to the first calculated length. Adjust the length of the tube by moving the inner tube in small increments in or out, until you hear the sound at its maximum amplification. Record the adjusted lengths as the Measured.

11) Repeat the procedure for the other calculated lengths.


 * Table B: Open Tube **
 * <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">open tube ||  ||   || ** % Error ** ||   ||   ||   ||
 * ** Frequency (Hz) ** || ** Harmonic Number ** || ** Length of tube – Calculated (Theoretical) ** || ** Length of tube – Calculated (Expeimental) ** ||^  || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">absolute difference m || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">length width end affect correction m || <span style="color: #000000; font-family: 'Calibri','sans-serif'; font-size: 14.6667px;">% error ||
 * ^  ||^   || ** (m) ** || ** (m) ** ||   ||   ||   ||   ||
 * 650 || 5 || 1.3375 || 1.371 || -2.5046729 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">-0.0335 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">1.2247 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">-11.9458 ||
 * 650 || 6 || 1.605 || 1.491 || 7.10280374 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.114 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">1.4922 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.080418 ||
 * 650 || 7 || 1.8725 || 1.75 || 6.54205607 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.1225 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">1.7597 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.55123 ||
 * 650 || 8 || 2.14 || 2.021 || 5.56074766 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.119 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">2.0272 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.305841 ||
 * 650 || 9 || 2.4075 || 2.275 || 5.50363448 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.1325 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">2.2947 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.8585 ||
 * 650 || 10 || 2.675 || 2.514 || 6.01869159 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">0.161 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">2.5622 || <span style="color: #000000; display: block; font-family: Calibri,sans-serif; font-size: 14.6667px; text-align: right;">1.881196 ||
 * Graph:**

analysis: In tubes, the anti node must be at the end for the sound to seem loudest. However there is typically chaos at the end of the tube and the larger the diameter the more the data will be shifted. because of this i calculated the theoretical length with the adjusted effects of the width and chaos. The relationship between the harmonic number and the length is liner direct and as one increases so does the other. Most of the problems were due to human error in perceiving loudness and temperature readings. Also the diameter of the tube was measured with a ruler and used to find how off the chaos should have made the data. This part of the lab could have been not accurate. the slope is equal to one half the lambda for the open tube and one fourth the lambda of the closed tube. if the temperature was calculated based on our experimental results the temperature would be off meaning the data is obscure. v/2f = slope. v/(2*650)=.253, v= 328.9 m/s

Calculations: there is chaos at the ends tube due to its diameter the wind. There must be an anti node at the end of the tube so that the sound can pass through the tube. if the tube ended with a node than the interference would cancel out the sound. if you plug in 11 into the slope of the line you would get .1287*11 =1.415 meters. You could plug in 10 to the equation of the line to get .2531*10 = 2.531 meters. )( This shows 5 half waves in the open tube, therefore there are 5/2 wavelengths in the tube, so the length of the tube is 5/2lambda
 * <span style="font-family: 'Times-Roman','serif'; font-size: 16px;">Discussion Questions **
 * 1) For an ideal resonance tube, an antinode occurs at the open end of the tube. What characteristic of real resonance tubes slightly alters the position of this antinode?
 * 1) Why must there be an antinode at the end of the resonance tubes?
 * 1) How long would the closed tube have to be to get the 11th harmonic?
 * 1) How long would the open tube have to be to get the 10th harmonic?
 * 1) Draw a figure showing the fifth resonance in a tube //closed// at one end. Show also how the length of the tube L5,is related to the wavelength, λ.
 * ( the line at the left end is the cap that keeps the tube closed, the parentheses are quarters of a wave. The length of the tube is related to the wavelength because at the 5th harmonic, there are 5/4 of a wave fitting in the tube so the length of the tube is 5/4lambda.
 * 1) Draw a figure showing the fifth resonance in an //open// tube. Show also how the length of the tube L5,is related to the wavelength, λ.

HW: Sound Waves:
Pitch and loudness are perceived measurements of sound waves. Pitch is related to the perceived frequencies and loudness is related to the amplitude. Frequency is in hertz = 1 vibration/ second. the faster the frequency the higher the pitch. Sound waves are introduced into a medium by vibrations. the disturbance travels from particle to particle passing along energy as it goes. The more force that goes into the original pluck the higher the amplitude. The amount of energy that is transported past a given area of the medium per unit of time is known as the intensity of a sound wave. The mathematical relationship between intensity and distance is an inverse square relationship. intensity is higher at closer distances. the threshold of human hearing is from 20 to 20,000 hz. the speed of sound can be measured as distance over time or by using the equation v= 331.5 +.6T where T is temp. the speed of sound is always faster in solids than other forms of materials. Natural Frequency: natural frequency is the frequency at which an object tends to vibrate when struck.these objects will produce sound waves. frequency is speed /wavelength. the linear densities of of strings also change speed and sound of waves. Vibrations can also be formed by the stick slip method where sound is produced through friction. when something vibrates with the same natural frequency as something else it often causes the other object to vibrate along with it. when two tuning forks of the same frequency are placed next to each other and one is hit the other will match its vibrations. Fundamental frequency is the frequency that results 1 harmonic(at first harmonic). Fundamental frequency also known as harmonic frequency. Harmonics represents the number of anti-nodes and the standing wave can specified by the harmonics. Nodal point in standing wave represents position of node. Anti-nodal point in standing wave represents position of anti-node. To find the specific harmonic frequency, just multiply the harmonic number and fundamental frequency. Length of string is equal to product of (1/2), wavelength and harmonic number. Musical instruments: a guitar has a few natural frequencies at which it will naturally vibrate. the natural frequencies depend on the tension of the string its linear density and the length of the string. open air columns have wave inside of different harmonics based on frequencies and length, the ends of the tubes are always anti nodes. The process of adding another anti-node and node to each consecutive harmonic in order to determine the pattern and the resulting length-wavelength relationship could be continued. the results should be consistent. Closed air columns on the other hand begin with a node and must end with an anti-node. this means it can only exist with odd harmonics or else both sides would have an anti-node and interfere with the sound produced. +

[]

=Lab: Reflection plane mirror:= Activity: Reflection in a Plane Mirror


 * Objectives: ** Demonstrate that reflection from a plane surce the angle of incidence is equal to the angle of reflection.


 * Materials: ** Optical Bench, Light source, circular reflecting surface, protractor, straight edge, compass, pencil, black tape, white and/or tracing paper.

The reflection of light from a plane surface is described by the law of reflection, which states that the angle of incidence, θi, is equal to the angle of reflection, θr, as can be derived by Fermat’s Principle. By convention, these angles are measured with respect to a line perpendicular to the plane surface. Reflection from a plane mirror or a flat transparent plane surface of a piece of glass or plastic are the most easily demonstrated examples of the law of reflection.
 * Theory **
 * Reflection **

In Figure 1(a) several rays are shown incident on a plane surface, and in each case the reflected ray is also shown. For each ray, the angle of incidence θi is seen to be equal to the angle of reflection θr.


 * Procedure **
 * Part A: Reflection **


 * 1) Place the ray box, label side up, on the guidesheet on this back of this paper. Adjust the light box so that only one beam of light exits the box. Line this up along the 10˚ line.


 * 1) Set the mirror so that its back is on the line.


 * 1) Trace the angle of reflection lightly, by making a few dots.


 * 1) Repeat for each angle of incidence.


 * 1) Extend all of the lines showing the ray directions until they intersect at one point. Using a protractor, measure the reflected angles θ//1r//, θ//2r//, θ//3//etc, for each of the rays. Record all these angles (to the nearest 0.1o) in the Data Table.

Analysis Calculate the difference (|θreflected//–// θincident|) between the measured values of the incident angle and the reflected angle for each of the three rays and record them in the Calculations Table.

Data Table 1: Reflection Analysis: The results of the experiment were very accurate and proved that the angle of reflection should be similar to the angle of the source.The small amount of difference was due to errors in drawing the lines, measuring the data and keeping the set up stable. Even with the sources of error, the percent error was very small and showed that the law of reflections is correct in theory.
 * **Ray** || ** Angle of Incidence, **** q **** 1 ** || ** Angle of Reflection, **** q **** 2 ** || ** Difference in Angle ** || ** Percent Error ** ||
 * ** 1 ** || 16.8 || 17.5 || .7 || 4.2% ||
 * ** 2 ** || 30.3 || 30.4 || .1 || .33% ||
 * ** 3 ** || 45.1 || 43.5 || 1.6 || 3.5% ||
 * ** 4 ** || 54.3 || 55.9 || 1.6 || 2.9% ||
 * ** 5 ** || 65.5 || 66.2 || .7 || 1.1% ||
 * ** 6 ** ||  ||   ||   ||   ||
 * ** 7 ** ||  ||   ||   ||   ||

Analysis Questions
 * 1) Are your data consistent with the law of reflection? State your answer as quantitatively as possible.

My data is very consistent with the law of reflection because the angles had very little difference which was caused by human error. The image is located at the back of the glass where the light is reflected.
 * 1) Where is the image in a plane mirror located?

The graph would be a straight line with a slope of one because the angles for the source and reflection(x and y axis) should be the same.
 * 1) If you were required to graph the angle of incidence vs. the angle of reflection, what would be the shape of the graph? What would the slope of the line be?

The images are reflected at the angle of viewing and show the light that is reflected back in the same angle. Images appear backwards because the light is reflected on the surface of the glass and is not projected.all planer images are virtual images that are up right and the same size. they are located inside the mirror at the same distance in front of the mirror.
 * 1) What are the characteristics of all images from plane mirrors?

measured distances: 2.5 inches in 2.34 inches out

= Lab: Curved mirrors = Objective: Demonstrate the focal properties of spherical reflecting surfaces

Data

(cm) ||
 * Object Distance (cm) || Focal Length (cm) || Calculated Image Distance (cm) || Experimental Image Distance
 * 48 || 5 || 5.5 || 5.4 ||
 * 18 || 5 || 6.9 || 6.6 ||
 * 23 || 10 || 17.7 || 17.3 ||
 * 48 || 10 || 12.6 || 12.6 ||

Hw: Light waves and reflection
a: Behaviors of light, Light can be reflected, refracted or diffracted. reflection is the projection of light off of a surface in the same angle that the light was received. Refraction is the change a wave undergoes as it changes from one medium to another. often the wave can speed up or change direction. Diffraction is the change in a wave as it passes through a small opening or curved surface. Light can also undergo interference, where different waves of light come in contact and disrupt each other. interference can also be constructive and cause a an addition of waves. In the diagram below constructive interference occurs wherever a thick line meets a thick line or a thin line meets a thin line. Polarized objects block out part of the light waves. they have streaks like a picket fence and block waves moving in one dimension. I f two polarized screens are paired and each block a different type of wave angle then they will block out all light. objects can be polarized by reflection or refraction. In wave interference models, whole numbers are associated with anti-nodes and half numbers are nodes. the difference in wavelengths for a interference to occur is found using a path difference equation. PD=S1-S2. anti-nodal points = m lambda where m is whole and for node points the numbers are .5, 1.5 etc. Young did a slit experiment and found patterns of light and dark lines although there were only 2 slits. Light bends around an obstacle or through an opening creates an interference pattern. Wavelength must be on the same order of magnitude as the opening of an obstacle. Lambda=10^-7 m The larger the opening the less interference. Less diffraction as opening decreases in size patterns will be closer together. Central anti-node is very bright (2x), double width fringe is the pattern to the right and left of the central antinode. Luminous objects are objects that can make a light themselves itself. Illumination objecs represent the objects that are not able to make a light themselves, but are able to reflect the light. Without light nothing can be seen We can see illumination objects when they reflect lights to our eyes. Line of sight means the direction of sight to see what you want to see. Incident ray: light that hit the object. Reflected light is light that is projected off on an object back at the viewer. The rule to mirrors is that things in the mirror appear to be the same distance away as they are to the mirror. The law of reflection stated that the angle between normal line, the line that is perpendicular to the surface of an object start from the point where incident ray hit, incident ray,angle of incident, is equal to the angle between normal line and reflected ray, angle of reflection. a persons line of sight is relative to where they are in relation to a mirror or the object they want to see. Mirrors are very useful for seeing images but often invert images and are only virtual. They cannot reflect an image back at something but can reflect the light of what is in front of it to show an image. if a mirror is curved or shifted it can alter images and cause magnification or distortion. from a persons line of view to the two extremes of a mirror show the amount of space that can be seen. []
 * [[image:http://www.physicsclassroom.com/Class/light/redboldlambda.gif width="7" height="8" align="bottom"]] = y • d / (m • L)**
 * Reflection of light:**

=Lab: refraction of light:= Objective: What is the relationship between the sin of the angle of incidence and the sin of the angle of refraction. Hypothesis: There should be a linear relationship between the two.




 * Analysis Questions**

>> The angle of incidence throughout the lab was always bigger when shooting the light through the air into the prism, as the data clearly shows that for a 10 degree angle going in, there is a 7 degree angle going out and so on.
 * 1) How does the angle of incidence compare to the angle of refraction when light travels from a medium of low optical density (air) to a medium of high optical density (acrylic)?
 * 2) Choose one: always bigger
 * 3) Provide evidence from the lab.

>> The lab shows that the angle of incidence from low to high is bigger, thus it is logical to assume that high to low yields smaller angles for incidence as the light would bend the opposite way.
 * 1) How does the angle of incidence compare to the angle of refraction when light travels from a medium of high optical density (acrylic) to a medium of lower optical density (air)?
 * 2) Choose one: always smaller,
 * 3) Provide evidence from the lab.


 * 1) What would happen to a light that entered the acrylic along the normal?
 * 2) The light refracted towards the normal.
 * 3) The light refracted away from the normal.
 * 4) The light only reflected off the plate.
 * 5)  The light did not refract, but went straight.


 * 1) Discuss how the angle of refraction changed with the angle of incidence. As the angle of incidence increased, the angle of refraction
 * 2)  Increased
 * 3) Decreased.
 * 4) Remained the same.Even though they increase at different rates, due to the equation nsin(theta)=nsin(theta) as one of the angles increases so will the other in order to keep the equation equal, even though they ma not increase at the same rate

Hw: mirrors
If the object is beyond than c the image will be real inverted, reduced and between f and c If the object is at c you get a real inverted same size image at c. Object between f and c, real inverted, enlarged, beyond c. At f there is no image Between f and v, virtual upright enlarged image behind the mirror. Image characters – two old super lions Type – real or virtual Orientation – upright Size Location
 * Converging mirror: concave**

Plane - flat – same size upright, equal distance, virtual, lateral inversion. Converging – concave <- virtual, upright, reduced image, located behind the mirror. Diverging – convex -> real, upside down small image, right side up large image. C= Center of curvature R = the distance to c, radius of curvature. F= the focal point, f = the focal length Focal length is half of the radius Di = image distance, do = object distance Hi = image height, ho = object height Hi/ho=-di/do=M A positive sign for di means the image is real and in front of t mirror. – di is behind the mirror. Positive image height means it is upright, negative image height means it is inverted. Negative focal length means diverging mirror. Practice.. Virtual reduced upright images that are between f and the mirror. convex mirrors do not form real images and show reduced size. It often reflects images away from the surface. The location of the object does not affect the characteristics of the image. As such, the characteristics of the images formed by convex mirrors are easily predictable. The images of objects formed by convex mirrors pertains to how a variation in object distance affects the image distance and size. Practice, more.
 * Mirrors**:
 * V =Vertex** – where the principle axis meets the mirror. Optical plane
 * Diverging mirror: convex**

Refraction: When an light wave switches medium it slows up or speeds up, changing its path. If the medium that the wave enters is less optically dense than the wave will move at an increased angle towards its target, it it is more dense than it will tilt slightly away. The refraction occurs only at the boundary. Once the light has crossed the boundary between the two media, it continues to travel in a straight line. Only now, the direction of that line is different than it was in the former medium. Light will travel straight if it enters the new medium at a 90 or 0 degree angle. Index of refraction are values that use somethings optical densities to determine lights speed compared to light in a vacuum. In refraction there are two angles, the angle of incidence and the angle of refraction.
 * < **FST = Fast to Slow, Towards Normal** If a ray of light passes across the boundary from a material in which it travels **f** ast into a material in which travels **s** lower, then the light ray will bend **t** owards the normal line. ||

Snell's law states that the angle of incidence and the angle of refraction can be found if the index of refraction values are known. where ("theta i") = angle of incidence ("theta r") = angle of refraction PRACTICE PROBLEMS =Lab: lens= Data
 * < **SFA = Slow to Fast, Away From Normal** If a ray of light passes across the boundary from a material in which it travels **s** low into a material in which travels **f** aster, then the light ray will bend **a** way from the normal line. ||
 * ni** = index of refraction of the incident medium
 * nr** = index of refraction of the refractive medium


 * Focal length of lens cm ||  || Object distance cm || Image Distance cm || Image Height cm || Object Height ||
 * 19.7 || Between F and 2F || 25.5 || 88 || 15 || 4.7 ||
 * 19.7 || At 2F || 39.4 || 39.7 || 4.4 ||  ||
 * 19.7 || Beyond 2F || 50 || 32 || 2.8 ||  ||
 * Focal length of lens cm ||  || Object distance cm || Image Distance cm || Image Height cm || Object Height ||
 * 10.5 || Between F and 2F || 18 || 25 || 5.7 || 4.7 ||
 * 10.5 || At 2F || 21 || 21 || 4.4 ||  ||
 * 10.5 || Beyond 2F || 40 || 13.7 || 1.5 ||  ||
 * Calculated Values ||  || Image Distance Lens 1 || Image Distance Lens 2 || Image Height Lens 1 || Image Height lens 2 ||
 * || Between F and 2F || 86.612 || 25.200 || 16.220 || 6.5277777778 ||
 * || At 2F || 39.400 || 21.000 || 4.736 || 4.7 ||
 * || Beyond 2F || 32.508 || 14.237 || 3.008 || 1.60975 ||
 * Percent Error || Image 1 Distance || Image 2 Distance || Height Image 1 || Height image 2 ||  ||
 * || 1.6024683985 || 0.7936507937 || 7.5193423598 || 12.6808510638 ||  ||
 * || 0.7614213198 || 0 || 7.0904121336 || 6.3829787234 ||  ||
 * Calculations:
 * || 1.6024683985 || 0.7936507937 || 7.5193423598 || 12.6808510638 ||  ||
 * || 0.7614213198 || 0 || 7.0904121336 || 6.3829787234 ||  ||
 * Calculations:

Image Distance Sample 1/f=1/di+1/do 1/f-1/do = 1/di (1/19.7-1/25.5 )^-1=di di= 86.612 CM || 1.5634517766

Calculations Image Height Sample. Di/Do=Hi/Ho (Di/do)Ho=Hi (39.7/39.4)*4.7=16.220cm || 3.7738095238 || 6.914893617 || 6.8178288554 ||  ||

Hw: Lens
If the object is beyond than c the image will be real inverted, reduced and between f and c If the object is at c you get a real inverted same size image at c. Object between f and c, real inverted, enlarged, beyond c. At f there is no image Between f and v, virtual upright enlarged image behind the mirror.
 * Converging lens:**

Virtual reduced upright images that are between f and the mirror.
 * Diverging lens:**

The **principal axis** of a mirror or lens is a normal that typically runs through the center of the mirror or lens. The **vertex**, represented by <span class="question_inline" style="font-family: 'Times New Roman',Times,serif; font-size: 12px;">//V// in the diagram, is the point where the principal axis intersects the mirror or lens.

Snells Law: Critical angles are the last angle where refraction is 90 degrees Animation: []

If n1=n2 than both angles are equal. If n1 >n2 slow, faster, away SFA If n1 < n2 fast, slow, towards FST Bigger the wavelength, the bigger the angle of refraction. Dispersion and scattering: upon passage through the prism, the white light is separated into its component colors - red, orange, yellow, green, blue and violet. The separation of visible light into its different colors is known as Dispersion. when light scatters it is projected in multiple directions. This is responsible for the color of the sky because light is scattered by the atmosphere. If speed drops, wavelength drops. Ratio for angles and index = n1/n2=λ2/λ1 Shorter λ are influenced less by a prism. Dispersion – spreading out of light into its component λ. The sky is blue because the atmosphere absorbs the light from the light and absorbs and reemits blue light in all direction. <span style="font-family: Arial,Helvetica,sans-serif; font-size: small;">The double convex lense is a converging lense. When light waves parallel to the principal axis from an infinitely far object passes through the lense, it will converge at a focal point F on the principal axis. The distance between the focal point and the lens is the focal length, which is always a positive value for converging lenses. <span style="font-family: Arial,Helvetica,sans-serif; font-size: small;">The double concave lens is a diverging lens. When light waves from an infinitely far object passes through the lens, the light waves will diverge as if it originated from a focal point F on the principal axis. The focal length is always a negative value for diverging lenses.

<span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%;"><span style="font-family: Arial,Helvetica,sans-serif;">The **focal length** is the distance between the principal focus and the optical centre of the lens. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%;">T<span style="font-family: Arial,Helvetica,sans-serif;">he **focal plane** is an imaginary plane perpendicular to the principal axis at the focal point. Parallel rays will converge through a converging lens somewhere on the focal plane. <span style="font-family: Arial,Helvetica,sans-serif; font-size: 80%;">Incident light rays are refracted twice by a lens; once at each boundary. Partial reflection may also occur. When the object is located at the 2F point, the image will also be located at the 2F point on the other side of the lens. When the object is located //in front of// the 2F point, the image will be located //beyond// the 2F point on the other side of the lens. When the object is located at the focal point, no image is formed. When the object is located at a location in front of the focal point, the image will always be located somewhere on the same side of the lens as the object.

Eye: Cornea: Opening of eyeball, Refract light. Protection. Pupil: Opening after the light came through the cornea. Iris: It controls the size of pupil., colored part of eye. It reduces openning in bright situation. Crystalline lens: made of layers of fibrous, index of refraction is approximately 1.4, double convex lens. Ciliary muscles: Helps to change the shape of lens to change the focal length. Retina: detects intensity and frequency of lights with rods and cones. Optic nerve: Network of nerve cells that connects the brain and eye. Fovea Centrails: the region that has greatest compacted rods and cones. Focal length of eye is about 1.8 cm. Accommodation represents the skills and abilities of eyes to adjust the focal length. The measurement of power of lens is diopter. Diopter is equal to 1/ focal length.