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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 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:
A, B
`mu=(sin((deltam+A)/(2)))/(sin(A/2))`
`cot""A/2=(sin((deltam+A)/(2)))/(sin""A/2)`
`(cos""A/2)/(sin""A/2)=(sin((deltam+A)/(2)))/(sin""A/2)`
`cos""A/2=sin((deltam+A)/(2))`
`therefore sin(90^@-A/2)=sin((deltam+A)/(2))`
`therefore 90^@-A/2=(deltam+A)/(2)`
`therefore180^@-A=deltam+A`
`therefore180^@-2A=deltam` `thereforedeltam=180^@-2A`
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