angle reflection physics question, please help :)

Question

We want light to reflect inside material 1 as it strikes the surface between materials 1 and 2. Material 1 has an index of refraction of n1=1.62 and material 2 has an index of refraction of n2=1.23. Find the smallest angle (from the normal) that will allow the ray to reflect internally to material 1. 
in terms of degrees. 
to a precision of tenths of a degree. 

Answer 1

What you want to find here is the critical angle θ_c.  Use Snell's law.  Are you familiar with it?

 

n₁sinθ₁ = n₂sinθ₂

 

To ensure full reflection into material 1, set 

 

θ₂ = 90°

 

Then θ₁ will be at the critical angle θ_c.

 

Snell's law becomes

 

n₁sinθ_c = n₂sin90° ⇒ n₁sinθ_c = n₂

 

sinθ_c = n₂/n₁

 

θ_c = sin^-1(n₂/n₁) = sin^-1(1.23/1.62) = 49.4°

 

(Note this happens only if n₂ < n₁)