The angle of incidence of a ray of light in air is adjusted gradually as it ente

Question

The angle of incidence of a ray of light in air is adjusted gradually as it enters a shallow tank made of Plexiglas and filled with carbon disulphide. The tank is open at the top, the ray of light passes directly from the air into the carbon disulphide. Is there a minimum angle of incidence for which light is transmitted into the carbon disulphide but not into the Plexiglas at the bottom of the tank?

If so, find the angle. If not, explain why not.

Index of refraction values are air: 1.000

Plexiglas: 1.51

carbon disulphide: 1.628

Explanation / Answer

For this to happen, we would need the total internal reflection of the light ray in the carbon disulphide as it hits the plexiglass. The formula for the cirtical angle to provide total internal reflection is

sinc = n2/n1 = 1.51/1.628

This will provide an angle of 68o, and that, in and of itself is possible, however...

To get an angle of incidence of 68o on the carbon disulfide/plexiglass interface, we would need that to be the angle of refraction between the air and carbon disulfide. Using Snell's law we can see

n1sin1 = n2sin2

If we try that, we get

(1)(sin1) = (1.628)(sin 68)

We would get...

sin1 = 1.51

And since the sin of an angle can be no larger that 1, you can see that this is impossible. Therefore, there is no possibility when the light ray will not enter the plexiglass at the bottom of the tank.

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