A light ray is partially reflected and partially refracted at a boundary between two media,the upper one having index of refraction n,the lower one having index of refraction n',as shown in the figure.The reflected ray is perpendicular to the refracted ray when
A) .
B) .
C) .
D) .
E) .

Question

A light ray is partially reflected and partially refracted at a boundary between two media,the upper one having index of refraction n,the lower one having index of refraction n',as shown in the figure.The reflected ray is perpendicular to the refracted ray when 
A) . 
B) . 
C) . 
D) . 
E) .

Quizplus · Accepted Answer

According to Snell's law, 
n*sin(θ1) = n'*sin(θ2)
where θ1 and θ2 are the angles of incidence and refraction, respectively. 
For perpendicular incidence, θ1=0, so sin(θ1)=0. 
Thus, we have 0=n'*sin(θ2), which means sin(θ2)=0 since n' cannot be zero. 
The only value of θ2 that satisfies sin(θ2)=0 is θ2=90° (or π/2 radians). 
Therefore, the refracted ray is perpendicular to the boundary, and the reflected ray is also perpendicular to the boundary (since it is symmetric to the refracted ray with respect to the normal). Hence, the correct answer is A.

A Light Ray Is Partially Reflected and Partially Refracted at a Boundary