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.