| n1sinQ1 = n2sinQ2 |  |
You will determine the index of refraction of three different substances utilizing Snell's law. The index of refraction, n, of a transparent substance is the ratio of the speed of light in vacuum to the speed in the substance. Since light travels fastest in vacuum, the index of refraction is always greater than one. When light travels from a transparent substance one index of refraction into a substance of a different index of refraction, the propagation speed changes. If the wavefront is oblique to the interface between the two substances, different parts of the wavefront will change speed at different times. The net result is a "bending" or refraction of the wavefront.
Snell's law relates the angle of incidence (Q1) to the angle of refraction (Q2) across a flat interface. It is given by
| n1sinQ1 = n2sinQ2 | |
The primary difference in each of the experiments below will be the method of determining the angles of incidence and refraction. You may assume the index of refraction of air to be essentially one.
Place one of the lucite blocks on a large sheet of white paper with the frosted side down. Turn on the laser and point it at one face of the block. Note how the beam refracts as it passes into the block. In order to clearly see the beam, you may have to position the laser close to the surface of table such that light scatters off the frosted surface.
Adjust the direction until you can clearly see the beam enter and then exit the block. With a pencil, trace around the block and mark several points along the laser beam that will allow you draw a ray for the beam as it enters and exits the block. Measure the angles of incidence and refraction at both surfaces with a protracter. Determine the index of refraction of lucite from both sets of angles. Estimate the error in determining the angles and estimate the resulting error in your calculations of the index of refraction. Are the two values the same within error?
Draw a straight line on a white sheet of paper. Center the glass block on top of line with the faces at an oblique angle to the line. Trace around the block. As you view the line through the block, it will appear to be displaced. Using a ruler or straight pins, mark the displaced image of the line. Remove the block and indicate the path of the ray through the block. Determine the index of refraction as in the previous section. (You may use a laser to help understand what is happening. Point the laser along the line and watch the path of the beam.)
A small object rests at the bottom of a beaker of water. Determine the index of refraction of the water using only rulers, protractors and your eyes. Clearly describe your method and provide diagrams indicating the mesurements you make.
Index Variations Using the SpectrometerA glass prism with 60o vertices is placed on a spectrometer table. A slit source of light provides a narrow beam of white light that strikes one face of the prism at 60o from the normal and exits an adjacent face as shown. The emergent beam is viewed through a pivoting telescope. The angle between the incident light and the emergent light can be read directly from the spectrometer scale. Look closely at the angles in the ray diagram for the prism. You will have to express Snell's Law at both interfaces in order to solve for the index of refraction of the prism. |  |
 | View the source through the telescope. You will notice that the white light has been spread out into its constituent colors. This occurs because the index of refraction is frequency dependent. Set the cross hairs in the telescope viewer and record the angles for 1) the far violet, 2) blue-green, 3) yellow, and 4) the far red. Calculate the index of refraction for each of these colors. What is the % spread in the values from far violet to far red? |