For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index

Options

A. lies between `sqrt(2)` and `1`
B. lies between `2` and `sqrt(2)`
C. is less than `1`
D. is greater than `2`

Answer

B

Explanation

From prism formula, `mu = (sin(A + delta_m)//2)/(sin A//2)`
For `delta_m = A`,
`mu = (sin A)/(sin A//2)`
=`(2 sin A//2 cos A//2)/(sin A//2) = 2 cos A//2`
When `A = 0^@, mu_(max) = 2 cos 0^@ = 2`
When `A = 90^@, mu_(min) = 2 cos 45^@ = (2)/(sqrt(2)) = sqrt(2)`
Choice (b) is correct.