9/22 Experiment 7: Introduction to Reflection and Refraction

We use a plastic semicircular shape and shine the light from one end and see the angle it changed due to the refraction of the light in different medium. According to Shell's law, the light will first been refracted due to the change medium from air to plastic, and refracted second due to the change medium from plastic to air again.

First part of the experiment is to shine the light from the flat surface of the plastic and measure the angle changed from the other end of the plastic

Second part of the experiment is to shine the light from the other way around, which is from the arc then measure the angle change from the flat surface

The data that we accuqired:

First
θ_1 (degree)	θ_2(Degree)	sin(θ1)	sin(θ2)
0	180	0.000	0.000
5	177	0.087	0.052
10	174	0.174	0.105
15	169	0.259	0.191
20	167	0.342	0.225
30	162	0.500	0.309
40	157	0.643	0.391
50	150	0.766	0.500
60	147	0.866	0.545
70	144	0.940	0.588
Second
0	180	0.000	0.000
5	175	0.087	0.087
10	163	0.174	0.292
15	155	0.259	0.423
17	150	0.292	0.500
20	147	0.342	0.545
25	138	0.423	0.669
30	128	0.500	0.788
35	117	0.574	0.891
40	103	0.643	0.974

If we graph θ_2 vs. θ_1  and sin(θ_2) vs. sin(θ_1)













According to Snell's Law
n_air*sin(θ1)= n_plastic*sin(θ2) = n_air * sin(θ3)

the θ we measure in experiment is the θ1 and θ3 which are the angle of light goes into the plastic and the angel comes out from the plastic.  The ratio of the sin of thetas will be the index of refraction of the plastic. From both experiments, the index of refraction is almost the same, which is around 1.5 to 1.58. This is within the uncertainties since we measure the average angle due to the light does not shine exactly. Even thought the theta vs. theta graph we fit with a linear graph, actual graph should look something different from linear. The graph should look something curvy. The reason the graph does not look perfectly curvy is the inaccurate of reading the degrees from protractor. Also, when we do the second part of the experiment, after certain degrees, the light will be trapped in the prism so we cannot measure the angle beyond the mmaximum incident angle.

9/8 Experiment 4: Standing Waves

Introduction:
In this experiment, a string is attached to a mechanism which give certain frequency that can generate

waves on the string. The velocity of the wave will be determine by the tension of the string and the mass

per unit length of the string. v=(T/u)^(1/2). The frequency of the mechanism will be adjust by a function generator that we can adjust the nob into the desire frequency

Analyze:

Constants u 0.001165kg/m Case 1 (w/ 123cm and 200.2g) 1 loop 2 loops 3 loops 4 loops 5 loops 6 loops 7 loops 8 loops 9 loops node 2 3 4 5 6 7 8 9 10 antinode 1 2 3 4 5 6 7 8 9 frequency(Hz) 17 36 51 71 86 104 122 140 158 wave length(m) 2.460 1.230 0.820 0.615 0.492 0.410 0.351 0.308 0.273 velocity(m/s) 41.82 44.28 41.82 43.665 42.312 42.64 42.87429 43.05 43.18667 avg velocity 42.84977 1.060431375 2.045551 1.060431 0.664596 0.289199 0.044004 0.000601 0.040091 0.113498 uncertainty 2.306166 Case 2 (w/ 131cm and 100g) 1 loop 2 loops 3 loops 4 loops 5 loops 6 loops 7 loops 8 loops 9 loops node 2 3 4 5 6 7 8 9 10 antinode 1 2 3 4 5 6 7 8 9 frequency(Hz) 11 ? 34 46 56 63 77 93 102 wave length(m) 2.620 1.310 0.873 0.655 0.524 0.437 0.374 0.328 0.291 velocity 28.82 #VALUE! 29.69333 30.13 29.344 27.51 28.82 30.4575 29.69333 avg velocity 29.30852 0.238652605 0.148081 0.674828 0.001259 3.234677 0.238653 1.320153 0.148081 2.450384

case 1
Theoretical velocity: 41.04m/s +- 0.17m/s


experiment velocity:43.07m/s +- 2.3 m/s

Both values are within their uncertainty, which they are consistent to each others

Case 2:
Theoretical velocity: 29.02 +-  0.23 m/s

Experimental Velocity :29.70+- 2.45m/s

Both values are within their uncertainties, which mean they agree with themselves


The ratio of velocities between case 1 and case 2 is about 1.38, which is close to radical 2 as we expected

Both cases' frequencies followed the patter of f = vn/2L  where v is the wave velocity, n is the number of antinode, and L is the length of the string. As we expected, when the wave lengths are the same, the lower velocity requires lover frequency inorder to reach certain resonance frequency. On the other hand, the higher the velocity requires higher frequency to reach the resonance frequency.

In case 1, the ration between first and second harmonic frequency is 2.11, and between second and thrid is 1.4, between third and fourth is 1.39. As we can see, the ratio decreases as the number of harmonic frequency increases. In case 2, it also has the same pattern occured.