Optics - Index of Refraction

A light source is at the bottom of a pool of water (the index of refraction of water is 1.33). At what minimum angle of incidence will a ray be totally reflected at the surface?

A. 0^o  
B. 25^o
C. 50^o 
D. 75^o
E. 90^o 

(GR9677 #56)

Solution:

Snell's Law: n_w sin θ_i = n_a sin θ_r

For total internal reflection, θ_r = 90^o
n_w sin θ_i  =  n_a
sin θ_i = n_a/n_w = 1/1.33 ≈ 3/4
Convert to degree, θ = ¾ × 180/π ≈ 45^o closer to 50^o 

Answer: C