Physics Question on Ray optics and optical instruments

Question

A ray of light passes through an equilateral glass prism in such a manner that an angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of prism. The angle of deviation is

Answer 1

Solution

According to the given information:
Angle of incidence (i) = Angle of emergence (e)
Angle of incidence (i) = Angle of emergence (e) = (3/4) * Angle of prism (A)
Using these relationships, we can set up the following equations: i=e (1)
i=e=(3/4)∗A (2)
The angle of deviation (D) is related to the angle of incidence and angle of emergence by the formula:
D=(i+e)−A (3)
Substituting equation (2) into equation (3), we get:
D=(3/4)∗A+(3/4)∗A−A
D=(3/2)∗A−A
D=A/2
From the given information, we know that each of the angles of incidence and emergence is equal to (3/4) of the angle of prism. Therefore, the angle of deviation is equal to half of the angle of prism.
Since the given prism is an equilateral prism, the angle of prism (A) is 60 degrees. Substituting this value into the equation for the angle of deviation, we get:
D=60/2=30 degrees
Hence, the correct option is (C) 30 degrees.