In this experiment we'll measure the refractive index of the plexiglass in the prism kit. You need to have:

• Laser ray box + power supply
• Circle mat
• Big semicircular prism
• Pencil, eraser
• Meter tape
• Paper triangle
• White screen
• Pencil

Take the big semicircular plexiglass prism, and on the bottom (mat) side, mark the center with a pencil

Put the semicircle on the mat with the pencil mark on the center.

Turn on the laser, and aim it at the center.

The incoming beam from the bottom right gets refracted, and exits the prism on the top left (and hits the screen, which is only there for safety)

Make a mark where the incoming ray crosses the big circle

... and a mark where the outgoing ray crosses the big circle

Turn off the laser, and remove the prism. Now we'll draw some lines.

Draw a line from the mark to the center line, using the triangle.

... and a line from the other mark to the center line, using the triangle.

This is the result.

The angle between the incoming ray and the vertical is called ${\theta }_1$ and the outgoing angle is ${\theta }_2$

Snell's law says this:

$\frac{sin{\theta }_1}{sin{\theta }_2}=\frac{n_2}{n_1}=\frac{v_1}{v_2}$

What does this mean? First let's look at $sin{\theta }_2$ . The sine of an angle is the ratio between the leg of the right triangle opposite the angle in question, and the hypothenuse (the leg of the triangle opposite the right angle). In the picture above, $sin{\theta }_2=\frac{b}{R}$
Similarly, $sin{\theta }_1=\frac{a}{R}$ , so if we divide the two, R drops out (because $\frac{\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$R$}\right.}{\raisebox{1ex}{$b$}\!\left/ \!\raisebox{-1ex}{$R$}\right.}=\frac{a}{b}$ )

and we can rewrite Snell's law like this:

$\frac{a}{b}=\frac{n_2}{n_1}=\frac{v_1}{v_2}$

What about n1 and n2? These are called the index of refraction, a property of the material that the light goes through. In our case, of air (incoming ray), and plexiglass (outgoing ray)

n is a number equal to 1.0 or greater. It says something about the speed v of light in that medium. The greater the number, the slower light travels in that medium. For vacuum (top speed) n=1. For air, it is a hair greater than 1.

So, what is the index of refraction n2 of plexiglass? If we substitute n1 with 1.0 (close enough), we have

So let's measure!

b = 53 mm

.... and

a = 79 mm

So the index of refraction of the plexiglass is 79/53 = 1.49

this means that light travels 1.5 times slower in plexiglass than in air (or vacuum).

  Vacuum       1
  Air          1.000293
  CO2          1.00045

  Aerogel      1.006 - 1.050

  Water        1.333
  Olive oil    1.47

  Ice          1.31
  Plexiglass   1.49
  Window glass 1.52
  Diamond      2.42
  Moisannite   2.65