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If the refractive index of a material of...

If the refractive index of a material of an equilateral prism is `sqrt3`, then angle of minimum deviation will be ..... .

A

`30^@`

B

`40^@`

C

`50^@`

D

`60^@`

Text Solution

Verified by Experts

The correct Answer is:
D
A=60, A+`delta_m=x`, n=`sqrt3`
For rquilateral prism n=`(sin(A+delta_m)/(2))/(sin(A/2))`
`therefore sqrt3=(sin(x//2))/(sin(60^@/2))`
`implies sin30sqrt3=sin(x//2)`
`implies sin(x//2)=(sqrt3)/(2)`
`thereforex/2=sin^(-1)((sqrt3)/(2))=60^@`
`thereforex=A+delta_m=120impliesdelta_m=120-60=60^@`
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