Question

A ray of light passes through an equilateral prism such that an angle of incidence is equal to the angle of emergence and the latter is equal to $\frac{3}{4}$ th the angle of prism. The angle of deviation is:

• A. $45{}^\circ$
• B. $39{}^\circ$
• C. $20{}^\circ$
• D. $30{}^\circ$

Answer 1

Answer: (D)

$30{}^\circ$

Answer 2

Angle of incidence = angle of emergence, i.e., $i = i'$
Also, $i' = \frac{3}{4}\times$ angle of equilateral prism $=\frac{3}{4}\times 60{}^\circ =45{}^\circ$
Thus, angle of deviation $= i + i' - A$
$=(45{}^\circ +45{}^\circ -60{}^\circ )=30{}^\circ$