Experiment 7: Introduction to Reflection and Refraction

The purpose of this experiment is to study the effects of a light ray as they pass though  a semicircular piece of plastic.  Light is bent because of the plastics index of refraction.

The Flat Surface

The first case is the angle of incidence is perpendicular to the flat surface.  There is no initial angle of refraction.  As the light ray leave the plastic the light will be refracted because of the change in medium form low density air to high density plastic.

Trial	θ1 deg	θ1 rad	θ2 deg	θ2 rad	Sinθ1	sinθ2
1	0	0	0	0	0	0
2	5	0.087266	3	0.05236	0.087156	0.052336
3	10	0.174533	6	0.10472	0.173648	0.104528
4	15	0.261799	9	0.15708	0.258819	0.156434
5	20	0.349066	12	0.20944	0.34202	0.207912
6	23	0.401426	15	0.261799	0.390731	0.258819
7	30	0.523599	13	0.226893	0.5	0.224951
8	35	0.610865	22	0.383972	0.573576	0.374607
9	40	0.698132	27	0.471239	0.642788	0.45399
10	45	0.785398	29	0.506145	0.707107	0.48481
11	50	0.872665	32	0.558505	0.766044	0.529919
12	60	1.047198	34	0.593412	0.866025	0.559193
13	70	1.22173	39	0.680678	0.939693	0.62932

Graph

θ­₁ vs θ­₂

A line equation fits this curve.

sin θ₁ vs sinθ­₂

The line equation is 1.43x+0.036.  The slope is the medium1/medium2 the y intercept suppose to be zero.

Curved Surface

The light ray hits the curved surface first.  When it hits the semicircle in initial position the light comes out un altered.  As angle increases the refraction increases. There will be an angle where the light will be internally refracted.

Trial	θ1 deg	θ1 rad	θ2 deg	θ2 rad	Sinθ1	sinθ2
1	0	0	0	0	0	0
2	3	0.05236	5	0.087266	0.052336	0.087156
3	6	0.10472	10	0.174533	0.104528	0.173648
4	9	0.15708	15	0.261799	0.156434	0.258819
5	12	0.20944	20	0.349066	0.207912	0.34202
6	15	0.261799	23	0.401426	0.258819	0.390731
7	13	0.226893	30	0.523599	0.224951	0.5
8	22	0.383972	35	0.610865	0.374607	0.573576
9	27	0.471239	40	0.698132	0.45399	0.642788
10	29	0.506145	45	0.785398	0.48481	0.707107
11	32	0.558505	50	0.872665	0.529919	0.766044
12	34	0.593412	60	1.047198	0.559193	0.866025
13	39	0.680678	70	1.22173	0.62932	0.939693
14	42	0.733038	90	1.570796	0.669131	1

When the angle of incidence reached 42 degrees the light did no come out.  The light was internally refracted.

Graph

sin θ₁ vs sinθ­₂

The equation is not the same.  The slope is the inverse relationship of the first equation.