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The refracting angle of a prism is A and...

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

A

`(180^(@)-3A)`

B

`(180^(@)+2A)`

C

`(90^(@)-A)`

D

`(180^(@)-2A)`

Text Solution

Verified by Experts

The correct Answer is:
D
`"As",mu=(sin""((A+delta)/(2)))/(sin(A/2))`
`impliescot(A/2)=(sin""((A+delta)/(2)))/(sin""(A/2))`
`implies(cos""(A/2))/(sin""(A/2))= ( sin"" ((A + delta)/(2)))/( sin ""((A)/(2)))`
`impliescos(A/2)=sin""((A+delta)/2)`
`implies sin(90^(@)-A/2)=sin((A+delta)/2)`
`implies90^(@)-A/2=(A+delta)/2`
`implies180^(@)-A=A+deltaimpliesdelta=(180^(@)-2A)`
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