The main goals of this experiment were to measure the index of refraction of a materials and to trace the path of a beam of light as it passes through several different geometries
The first part of the procedure was to align the beam of light that would be used for the rest of the experiment. The result was a single beam of light perfectly aligned with the 00-00 axis of the optical disk.
The first part of the experiment tested the accuracy of the alignment of the optics. This was done by placing a plane, convex, and concave mirror on the optical disk. The placement ensured that the point where the light met the mirror was exactly at the center of the disk, and that the mirror was aligned to the 900-900 axis. It was a painstaking process for both me and my group mates. The experimental set-up was so sensitive, especially considering that our bare hands were not the most precise means to manipulate it.
The results may be seen below.
As seen from the table above, the optics were now completely aligned. The interesting part, however, is not that the plane mirror have the same angles of incidence and reflection, but that the convex and concave mirrors displayed this as well. Because infinitesimally small planes essentially comprise curved surfaces, the angles of incidence and reflection of curves consequently follow the same laws as those for plane surfaces. This is provided that the beam of light is relatively thin and the point of reflection is perfectly perpendicular to the said beam.
Next, the index of refraction of a cylindrical lens was calculated. The driving concept here is Snell’s Law. It is described in the equation below:
where theta 1 and theta 2 describe the angle of incidence and refraction, respectively, and n1 and n2 describe the indices of refraction of the incident and refractive mediums respectively. First, the experiment was performed with the beam striking the plane side of the lens.
The data was then graphed and linearized according to Snell’s Law.
The slope of this equation is equal to the ratio of the index of refraction between the two mediums. At STP, the index of refraction for air, the incident medium, is about 1. Therefore, the index of refraction of the cylindrical lens is 1.4767. The resulting equation also has an R^2 value of 1. This shows that the experiment had a high degree of precision.
Next, the same experiment was performed, except the lens was rotated 180 degrees, with the curved surface facing the beam.
The data is shown in the graph below. It was analyzed in the same manner as the results from the tests using the flat side of the lens.
The high R^2 value also denotes a high degree of precision. An interesting observation arises: the value of the index of refraction, which is now 0.5938, has changed after the change in the orientation of the lens as it is hit by the incident beam. This may be attributed to the change in angle due to the change in the apparent geometry of the lens.
The critical angle is defined to be the angle at which the medium no longer refracts light. In this instance, it was experimentally determined to be 42.5 degrees.