Consider the optical interface between crown glass & ethanol.?

Question

- Under what conditions would total internal reflection be possible at this interface? Illustrate your answer with a light-ray diagram, or simply explain it in your own words.
- What light travels from crown glass into ethanol? If the angle of incidence of crown glass is 60.00 degrees, what is the angular spread between the red and violet parts of the visible spectrum in the ethanol? Illustrate with a light-ray diagram or explain in your own words.
- Light travels from ethanol into crown glass. What is the Brewster angle in this situation? Illustrate your answer with a light-ray diagram. What is the significance of this angle of incidence?

Answer 1

A ray of light travelling to the crown glass / ethanol interface at an angle > θc with respect to the normal to the surface will be reflected internally.

The critical angle θc can be calculated

θc = arcsin (RI(ethanol) / RI(glass))

Refractive Indices
RI(ethanol) = 1.36
RI(crown glass) = 1.52

The second part of the question requires Snell's Law

n1 sin(θ1) = n2 sin(θ2) and is simply a matter of calculating θ for red and violet to determine the angular spread.

Regrettably the relevant data (velocities or refractive indices for red and violet light in the various media) is not to hand, nor easily obtainable. Perhaps the questioner would be so kind as to supply it.

The third part of the question - Brewster's angle can be calculated for the two media using the formula

θB = arctan (RI(glass) / RI(ethanol)) = arctan (1.52/1.36)

This angle signifies the angle at which s-polarized light is reflected from the interface with no p-polarized light being transmitted.