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

Options

A. `-180cm-3A`
B. `-180cm-2A`
C. `-90cm-2A`
D. `-180cm+2A`

Answer

B

Explanation

(b) Refractive index,`mu=sin((A+D_(m))/2)/(sin""A/2)`
`rArrcot""A/2=sin((A+D_(m))/2)/(sin""A/2)`
`rArr(cot""A/2)/(sin""A/2)=sin((A+D_(m))/2)/(sin""A/2)`
`sin((pi)/2-A/2)=sin((A+D_(m))/2)`
`pi/2-A/2=A/2+(D_(m))/2`
`rArrD_(m)=pi-2A`
Angle of minimum deviation, `D_(m)=180^(@)-2A`