Experiment 7: Introduction to Reflection and Refraction

The purpose of this experiment is to analyze how a beam of light is reflected and refracted as it enters and exits a semicircular plastic. First we will take a light box and set it up so only a single beam will be emitted. We will then measure the angle of incidence as the beam of light enters the plastic and the angle of refraction as the beam of light exits the plastic.

First we began the experiment so that the light entered the flat side of the of the semicircular plastic. Our first trial would have the light entering at zero degrees to the normal of the flat side. We then measure the angle of refraction as the light exited the semicircular side. We took ten trials were on each trial we increased the angle the light entered the flat side from its normal. After all ten trials were were left with angles Theta_1 (the angle the light made with the normal on the flat side) and Theta_2 (the angle the light made when it was refracted our the curved side). We then calculated sin(Theta_1) and sin(Theta_2) for the corresponding values of Theta. Our recorded results are below.

Trial	Theta_1 (degrees) +/-1.5	Theta_2 (degrees) +/-1.5	sin(Theta_1) (radians)	sin(Theta_2) (radians)
1	0	180	0	0
2	5	177	0.087	0.052
3	10	174	0.174	0.105
4	15	170	0.259	0.174
5	20	167	0.342	0.225
6	30	162	0.5	0.309
7	40	157	0.643	0.391
8	50	150	0.766	0.5
9	60	147	0.866	0.545
10	70	144	0.940	0.588

Next we did anther ten trials except this time the plastic semicircle was turned 180 degrees so that the light entered the semicircular side and exited the flat side. The trials are shown below.

Trial	Theta_1 (degrees) +/-1.5	Theta_2 (degrees) +/-1.5	sin(Theta_1) (radians)	sin(Theta_2) (radians)
1	0	180	0	0
2	5	175	0.087	0.087
3	10	163	0.174	0.292
4	15	155	0.259	0.423
5	17	150	0.292	0.5
6	20	147	0.342	0.545
7	25	138	0.423	0.669
8	30	128	0.5	0.788
9	35	117	0.574	0.891
10	40	103	0.643	0.974

We then plotted graphs of sin(Theta_1) versus sin(Theta_2) for each of the two data sets.





These two graphs show that there is a linear relationship between the angle at which light enters a surface and at which it exits the other side. This can also be described by Snell's Law which states n_air*sin(θ1)= n_plastic*sin(θ2). By looking at our graphs we can also tell what the index of refraction of the light through the plastic semicircle was somewhere between 1.55 and 1.59 when inaccuracies were taken into account. This gives us and average refraction of light to be 1.57 which is close to the expected index of refraction of a plastic.

Experiment 4: Standing Waves

The purpose of this experiment is to gain understanding of standing waves in a string and how the tension, length of the string, and the frequency of the wave being propagated through the string effect the number of standing waves in the string. Furthermore this will allow us to understand the resonant conditions of our string.

We began experiment by setting up the apparatus which consisted of a length of string with one end attached to a a mechanical oscillator which was connected to a wave generator. The other end of the string hung over a pulley with an attached weight. This caused the string to be under tension as waves propagated through the string. The hanging mass would be 100 grams for a series of ten trial ans 200 grams for another ten trials. The uncertainty for each of the masses was +/- 1.0 grams. The frequency of the wave would be read from the wave generator. The uncertainty of the recordings from the wave generator was +/-0.5 Hz. After ten trials for each mass we recorded the following chart.

At 100 grams:

# of Standing Waves	Frequency (Hz) +/-0.5
1	11
2	?
3	34
4	46
5	56
6	69
7	77
8	93
9	102
10	?

At 200 grams:

# of Standing Waves	Frequency (Hz) +/-0.5
1	16
2	30
3	46
4	64
5	79
6	96
7	110
8	126
9	144
10	?

As you can see we were unable to obtain readings for some of the standing waves. This is likely because waves were bouncing back and causing some destructive interference at some frequencies. This interference can only we eliminated with a apparatus better suited for this experiment. However the apparatus satisfies our basic needs for this experiment.

When we plot the frequency of the wave versus the inverse of the wavelength we obtain a liner relationship as shown by the following graphs.

Using this relationship v=f(lamda) we found the velocity of the wave at each of the given tensions. At 100g we found v to be about 14.9 m/s and at 200g to be about 20.5 m/s. We then used the equation v=sqrt(T/mu) to compare our velocities. We took mu to equal 0.0035 kg/m. At 100g we found or velocity to then be 16.7m/s and at 200g the velocity was 23.68m/s. This gives us a percent difference of 10% at 100g and 13% at 200g. This percent error can be explained to our inaccuracies in the recordings, the string not having a consistent density, and the wave generator not producing waves at exactly the recorded frequencies.