A ray in oil (n = 1.52) reaches a boundary with water (n = 1.33) at 55.9 deg. Does it reflect internally or refract into the air?

Question

Enter 0 for reflect, and 1 for refract.

(Water n = 1.33, Air n = 1.00)

Answer 1

A ray will be internally reflected if the angle of incidence to a boundary is greater than the critical angle. The formula for determining the critical angle is given by sin θ_c = n₂/n₁ where n₁ is the index of refraction for the incident medium and n₂ is the index of refraction for the refracting medium.

sin θ_c = 1.33/1.52 = 0.875

θ_c = 61.0° The incident angle is less than the critical angle, so the ray will be refracted into the water, the refracting angle being 71.1°. The angle of incidence to the water layer will be 71.1°. The critical angle for water to air is 48.8°, so the ray at this point will be reflected.