What Is the Maximum Angle of Incidence for Light in Diamond?

[dranseth]

Homework Statement

A cubic container contains air, water, glycerin, amd diamond. There are no spaces between, and all boundaries are parallel. For light to travel through all of the substances, what is the maximum angle of incidence of the light ray in the diamond?

Homework Equations

(n)(sin(critical angle))=(n)(sin(90º)
n= index of refraction

The Attempt at a Solution

Basically, I drew it out, found all the critical angles, got confused, then came here.

 

[Shooting Star]

Start with considering the emergent ray in the air, and let that one get out at 90 deg in the air. So, the ray from the water to air is at the critical angle. Now work your way backward.

 

[dranseth]

I don't understand.

 

[Shooting Star]

The light ray travels from the diamond to glycerin to water to air. If at any of the interfaces, the angle is greater than the critical angle between those two media, it'll be reflected back and won't reach the air. At the last interface, that is, between water and air, it can just come out at 90 deg.

Note that the densities of the materials are also in same order as the RIs of the materials, so the light ray keeps on bending to the same side.