A light ray in air strikes a glass surface with an angle of incidence of 30.0$^{\circ}$.The angle of refraction in the glass is 20.0$^{\circ}$.What is the angle between the reflected ray and the refracted ray?
A) 60$^{\circ}$
B) 70$^{\circ}$
C) 120$^{\circ}$
D) 130$^{\circ}$
E) 140$^{\circ}$

Question

Quizplus · Accepted Answer

By the law of reflection, the angle of incidence with respect to the normal is equal to the angle of reflection with respect to the normal. So the angle between the incident and reflected ray is also 30 degrees. 
By Snell's law, we can relate the angles of incidence and refraction to the indices of refraction:
n_air sin(theta_i) = n_glass sin(theta_r)
Here, we are given theta_i = 30 degrees and theta_r = 20 degrees. The index of refraction for air is approximately 1, while the index of refraction for glass is around 1.5. Substituting these values, we can solve for the sine of the angle between the reflected and refracted rays:
sin(alpha) = sin(theta_i - theta_r) / sin(theta_i + theta_r) = sin(10 deg) / sin(50 deg)
Using a calculator, we find that sin(alpha) = 0.1736, which implies that alpha = 10 degrees. 
Therefore, the angle between the reflected and refracted rays is 30 + 10 + 20 = 60 degrees. The correct answer is (D).

A Light Ray in Air Strikes a Glass Surface with an Angle