Light ray passing thru plastic block

[herbally]

Homework Statement

A light ray passes downward into a block of transparent plastic with an angle of incidence of θ₁ = 77.7°.

If total internal reflection is to occur when the light strikes the left edge of the block at interface B, what is the index of refraction of the plastic?

Homework Equations

Snell's Law - n₁sin(θ₁)=n₂sin(θ₂)

sin(θ_crit)=n₂/n₁

The Attempt at a Solution

I thought that I could use the law of refraction at interface A and the equation for the critical value at interface B (since total internal refraction occurs there), and use those two equations to solve for n₂. I've done all manners of substitutions, but nothing that yields a reasonable answer.

I would really appreciate a nudge in the right direction.

Thanks in advance!

 

[TSny]

Hello.
Your outline of how to approach the problem sounds good. Can you show your work so we can see what you've done?

 

[herbally]

I solved Snell's law for sin(θ₂) which yielded n₁sin(θ₁)/n₂.

I set that equal to n₂/n₁. Then I solved for n₂ which gave me n₂=+-n₁√sin(θ₁).

When I solve I get some value like .98755 which is less than one making it obviously incorrect.

 

[TSny]

I think you're using the same symbol θ₂ for two different angles.