Introduction to Reflection and Refraction

Purpose:
We are going to observe the phenomenon of reflection and refraction of light different medium and different angle.


1. We have the light ray goes to the center of semicircular plastic in flat surface and protractor.

Predicted data:

We have the angle of incidence for light ray at flat surface is 0º, the angle of refraction for light ray at flat surface is 180º.

The light ray leaves the plastic piece at curved edge get dimmer when it leaves plastic piece at curved edge and goes into the air as as some amount of light ray reflected at the curved edge so less amount of light ray goes into the air.

The light ray travels from lower density to higher density from air to plastic and higher density to lower density from plastic to air.

The light ray behave as we predicted as the light ray get dimmer when it leaves the curved edge of plastic and goes into air.

We measure the angle of incidence θ_1 and angle of refraction θ_2 and rotate the prism and protractor by a small amount every trial.

Experiment data:

We have the data of angles:

Trial	θ_1(º)	θ_2 (º)	sin(θ_1)	Uncertainty of sin(θ_1)	sin(θ_2)	Uncertainty of sin(θ_2)
1	0 ± 0.5	180 ± 0.5	0	0.5	1.22515E-16	-0.5
2	5 ± 0.5	178 ± 0.5	0.087156	0.498097	0.034899497	-0.4997
3	10 ± 0.5	173 ± 0.5	0.173648	0.492404	0.121869343	-0.49627
4	18 ± 0.5	169 ± 0.5	0.309017	0.475528	0.190808995	-0.49081
5	26 ± 0.5	167 ± 0.5	0.438371	0.449397	0.224951054	-0.48719
6	34 ± 0.5	159 ± 0.5	0.559193	0.414519	0.35836795	-0.46679
7	42 ± 0.5	155 ± 0.5	0.669131	0.371572	0.422618262	-0.45315
8	50 ± 0.5	150 ± 0.5	0.766044	0.321394	0.5	-0.43301
9	60 ± 0.5	145 ± 0.5	0.866025	0.25	0.573576436	-0.40958
10	70 ± 0.5	140 ± 0.5	0.939693	0.17101	0.64278761	-0.38302

I think the straight line equation y=mx +b will fit this curve.

The graph:



The slope of graph is 1.462, and it represents the refractive index of plastic.

Substitute two points of the graph, the slope m will be m=(0.939693-0)/(0.64278761-1.22515E-16) ,m=1.461902789, to solve b , I put one point into equation, 0.087156=(1.461902789)(0.034899497) + b and b= 0.036136328, so I have relationship of the equation y=1.462x + 0.03614.

2. We have the light ray goes to the center of semicircular plastic in curved surface and protractor.

Expected data:

The light ray may become dimmer when it enter curved surface of the semicircular prism as there is some amount of light ray reflected at the curved surface.

The refracted light ray at the flat surface disappears when the protractor and prism is rotated into some certain value of angle.

The light ray travels from lower density to higher density from air to plastic and higher density to lower density from plastic to air.

We measure the angle of incidence θ_1 and angle of refraction θ_2 and rotate the prism and protractor by a small amount every trial.

We have the data of angles:

Trial	θ_1 (º)	θ_2 (º)	sin(θ_1)	Uncertainty of sin(θ_1)	sin(θ_2)	Uncertainty of sin(θ_2)
1	0	0	0	0.5	0	0.5
2	8	12	0.139173	0.495134	0.207911691	0.489074
3	16	24	0.275637	0.480631	0.406736643	0.456773
4	24	40	0.406737	0.456773	0.64278761	0.383022
5	32	53	0.529919	0.424024	0.79863551	0.300908
6	40	75	0.642788	0.383022	0.965925826	0.12941
7	48	133	0.743145	0.334565	0.731353702	-0.341
8	56	124	0.829038	0.279596	0.829037573	-0.2796
9	64	115	0.898794	0.219186	0.906307787	-0.21131
10	70	110	0.939693	0.17101	0.939692621	-0.17101

The graph:



We cannot complete all 10 trials. We find the reflected ray disappears at the 5th trial. The graph is shown as "z" shapes after the data based on the 5th trial, which does not make sense as sin(θ_1) and sin(θ_2) should be proportional.

We should omit the points after the 5th trial. We have the new graph:



The slope is 0.651, and it represents the refractive index.

The slope of graph is 1.462, and it represents the refractive index of plastic.

Substitute two points of the graph in the first 5th trial, the slope m will be m=(0.139173-0)/(0.207911691-0) ,m=0.669385157, to solve b , I put one point into equation, 0.275637=(0.669385157)(0.406736643) + b and b= 3.373528368 E^-3, so I have relationship of the equation y=0.670x + 3.3735 E^-3, which is different from the equation from step 7 y=1.462x + 0.03614.

Conclusion:
We successfully observe the phenomenon of reflection and refraction of light different medium and different angle. For the part of light ray enters flat surface of plastic, we have the experimental behavior of light ray matches to the predicted behavior of light ray.We find the the the sin(θ_1) and sin(θ_2) is proportional relationship, and the ratio of them is refractive index. We find the refractive index of plastic is almost a constant. For the part of light ray enters curved surface of plastic, we have the experimental behavior of light ray matches to the predicted behavior of light ray. We cannot find the angle of refracted after the 5th trial as the refracted angle disappear because it reaches internal total reflection, which matches the predictions. We still can find the proportionality of sin(θ_1) and sin(θ_2) and reflective index of plastic by neglecting the data after the 5th trial.