Experiment # 7: Introduction to Reflection and Refraction

Using a light box and a half cylinder of acrylic, it is possible to observe light's behaviour when it changes mediums.

 

In this experiment, the acrylic object is rested on top of a paper protractor. Then the incident and refracted angles are recorded.

As always, the data associated with this experiment can be found in my Google documents folder here. The uncertainty associated with each angle measurement is plus or minus a half degree.

From the data, it appears that there are two observable trends as illustrated by the following graphs.

These graphs represent a plot of the refracted angle (Theta 2) vs. the angle of incidence (Theta 1). The graph which is titled air to acrylic represents the data collected when the light hits the flat part of the acrylic first, and the chart titled acrylic to air represents when the light hits the rounded side of the acrylic first.

First thing of note, both of these graphs have a relatively linear trendline, as demonstrated by their regression numbers(R^2 on the graph). Unfortunately, they both have non-zero intercepts with the vertical axis. Also, both appear to have some curvature in their data points as the angle increases.  This leads me to believe that the linear relationship between the refracted angle and the incident angle only applies when the small angle approximation can be used. (angles less than 30 degrees)

Additionally, it is interesting to note that the slopes of both graphs are nearly the inverse of each other.v(within 10 percent)

When the Sine of the angles are plotted against each other, a clearer picture begins to form.

 

 This relationship has a demonstrably more linear relationship, because the regression numbers are much closer to unity than the straight angle to angle relationship. Additionally, the intercepts with the vertical axis are almost zero, which supports the experimental data. (In both data sets, the point 0,0 appears).

Also, the slopes of these lines are closer to the inverse of each other.(2 percent deviation)

In titling these charts, it is important to note that the description of the interface applies to when the light contacts the linear part of the acrylic disk. When the light enters or exits the acrylic disk through the rounded portion, no refraction occurs because it always has an angle of incidence of zero. This is assuming that the light enters the disk aimed at the mid point of the linear portion of the disk, which is the case for the entirety of both data sets.

Observations:

The slope of the graph was greater when the light travelled from the acrylic to the air. Additionally, the slopes of each graph are very nearly the inverse of one another. This leads me to believe that there is some constant which represents a ratio between the sine of the angle of incidence and the sine of the angle of refraction.

According to Sears and Zemansky's University physics, the relationship between the angle of incidence and the refracted angle does depend on the sine of both angles, and is modified by 2 constants. It takes the following form:

where v1 is the velocity of light in medium 1 v2 is the velocity of light in medium 2 and n1 and n2 are some constants which describe the refractive property of a given medium.

Air is said to have a refractive index of nearly 1, so it is apparent that the acrylic disk used for the experiment has a refractive index of 1.466. Furthermore, this measurement is consistent with reported indexes of refraction for acrylic glass which fall in the range of 1.490 - 1.492. (error =1.6-1.7%)