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The refracting angle of a prism is A, an...

The refracting angle of a prism is A, and refractive index of the material of the prism is cot `(A // 2)`. The angle of minimum deviation is

A

`180^(@) - 3A`

B

`180^(@) - 2A`

C

`90^(@) - A`

D

`180^(@) + 2A`

Text Solution

Verified by Experts

The correct Answer is:
B
`"We know" , mu = sin""(A + delta_(m))/(sin""(A)/(2))`
`or, sin""(A + delta_(m))/(2) = mu sin""(A)/(2) = cot""(A)/(2) sin""(A)/(2)`
`= cos""(A)/(2) = sin(90^(@) - (A)/(2))`
`therefore (A + delta_(m))/(2) = 90^(@) - (A)/(2)`
`or, " " A + delta_(m) = 180^(@) - A or, delta_(m) = 180^(@) - 2A`
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