Question

An equilateral prism is made of a material of refractive index \( \sqrt{2} \). Find the angle of incidence for minimum deviation of the light ray.

• A. \( 60^\circ \)
• B. \( 30^\circ \)
• C. \( 37^\circ \)
• D. \( 45^\circ \)

Hint:

In prism refraction problems, use the relation between the refractive index and the angles of the prism and deviation to find the required angle of incidence.

Answer 1

The Correct Option is A

For an equilateral prism, the angle of the prism \( A = 60^\circ \). The refractive index \( n = \sqrt{2} \). Using the formula for the angle of incidence for minimum deviation: \[ \sin \left( \frac{A + D}{2} \right) = \frac{n}{\sin \left( \frac{A}{2} \right)} \] where \( A \) is the angle of the prism and \( D \) is the angle of deviation. By solving this equation, we find that the angle of incidence for minimum deviation is \( 60^\circ \).