Introduction to Reflection and Refraction

Purpose:

            The purpose of this experiment it to further understand the behavior of light as it passes through different mediums. In addition, we will also be exploring the affects of the incident angle and to what extent light can enter a medium before it can no longer be refracted outward.

Procedure:

1.      The following supplies were gathered up:

a.       Box of acrylic shapes

b.      Light source with adjustable light filter

c.       Paper protractor

2.      The light source was hooked up to the power supply and the paper protractor was laid down in front of the light source – with 0^o meeting at the incidence of the light – with an acrylic semi circle placed on top. The flat side was placed in the front path of the incoming light.

3.      The semi circle was then rotated – along with the paper protractor – about the incoming light.

4.      The angle at which the light entered was recorded as well as the angle at which the light exited the semi circle. This was done for ten different angles with each increment varying.

5.      The same process for steps 2 – 4 were repeated but this time the light of incidence was at the opposite end of the semi-circle, the curved end now was considered the point of entry for the light.

Data Analysis:

           

            Part A

            For this part, I will be referring to the process in which the incident light entered from the flat end of the semicircle. The defined angle of incidence for this procedure was 0^o and the angle of refraction was defined at the 180^o mark (all of the values for the refracted angle were measured and then subtracted from 180 to obtain the true degree of refraction). The light was going from the air into the acrylic and then back out into the air again. The light was therefore traveling from a source of low density into a medium of high density then once more back into the low density medium. This change in density will then cause the light to bend either away from the normal (when entering higher density) or towards the normal (when entering a lower density). This bend is what is defined as refraction. For the initial run, when the surface was set to zero degrees, the light was not refracted at all. Rather, the light continued to travel along its straight path. This is because the light was entering the semicircle along the normal angle relative to the surface and therefore had to direction in which to deflect ( as seen in the 1st picture).

The semicircle was then rotated and the deflected angle was recorded in a table. This process was done 10 different times with 10 different angles, each one increasing until reaching a maximum angle of 70^o. These angles are as followed:

Trial	Θin	Θout
1	5 ± 0.5	2± 0.5
2	10± 0.5	7± 0.5
3	15± 0.5	11.5 ± 0.5
4	20± 0.5	15± 0.5
5	25± 0.5	18± 0.5
6	30± 0.5	21± 0.5
7	40± 0.5	26± 0.5
8	50± 0.5	31± 0.5
9	60± 0.5	36± 0.5
10	70± 0.5	41± 0.5

These angles were then plotted into a graph against one another for further comparison.

Once that was done, the sin of the each angle was then computed and plotted against each other.

Trial	Sinθin	Sinθout
1	.087	.035
2	.174	.122
3	.259	.199
4	.342	.259
5	.423	.309
6	.500	.358
7	.643	.438
8	.766	.515
9	.866	.588
10	.910	.656

As you can see from the graph, the slop of the best fit linear line is 1.453. This number is very important because it corresponds to a number of things. It is the ratio of the sine of the angles and is also the index of refraction for the acrylic medium. The index of refraction of acrylic is actually 1.49 which is means that our experimental is only off by a factor of .01 or about 2.5% error.

            Part B

For this next part of the experiment, the incident light was now entered through the arched rim of the semicircle. The same defined angles of incidents were used as the pervious part. When the acrylic was lined up and the light turned on, the light still did not deflect. This is because of the same reason as before. Although the surface was curved, the light still entered through the normal which lead for it not to deflect.

Once again, the semicircle was rotated and the refracted light and incident light angles were recorded for 10 different angles. However, once we reached a critical angle (~42^o) the light no longer refracted out of the semicircle.

This is because at this critical angle, total internal reflection (TIR) is achieved. This means that the light angle bent outward of the acrylic is equal to the angle of the positon of the glass relative to the outside air, causing the light to bounce back within the acrylic itself and not allowed to pass through it (the light in the picture outside of the semicircle is not refracted light but rather reflected light). This angle is 90^o which is just perpendicular to the normal and parallel to the surface of the semicircle along the edge. The values were recorded up to this point and are displayed in the table below as well as with the values for the calculated sine values of the angles.

Trial	Θin	Θout	Sinθin	Sinθout
1	5± 0.5	4± 0.5	.087	.070
2	10± 0.5	12.5± 0.5	.174	.216
3	15± 0.5	20± 0.5	.259	.342
4	20± 0.5	27± 0.5	.342	.454
5	25± 0.5	39± 0.5	.423	.629
6	30± 0.5	52± 0.5	.500	.788
7	40± 0.5	84± 0.5	.643	.995
8	42± 0.5	90± 0.5	.669	1.00

The values of the calculated sine angles were then calculated and plotted against each other to display their linear relationship.

As depicted in the graph, the line equation is:

y = .5823x +.05478

Clearly, this is not the same as the previous graph. This is because of the curvature of the semicircle as the light is exiting the acrylic.

Summary:

            Throughout this experiment, we explored many different characteristics of light. The first part of this experiment showed how light, when traveling on a path normal to the surface will continue to travel in that direction, regardless if the surface is curved or flat. We also explored the property of TIR in which light gets totally reflected inside the material and none of it gets refracted. Lastly, we explored the property of index of refraction for different mediums and how it relates to the angle in which they enter and leave that medium.