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The refracting angle of the prism is 60^...

The refracting angle of the prism is `60^(@)`.What is the angle of incidence for minimum deviation? The refractive index of material of prism is`sqrt(2)`.

A

`60^(@)`

B

`45^(@)`

C

`30^(@)`

D

`40^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
`n = ( sin ((A + delta_(m))/(2)))/(sin ((A)/(2)))`
But `n = sqrt2 , sin ((A)/(2)) = sin 30^(@) = (1)/(2)`
`therefore sqrt2 xx (1)/(2) = sin ((60^(@) + delta_(m))/(2))`
`therefore (1)/(sqrt2) = sin ((60^(@) + delta_(m))/(2))`
`therefore sin 45^(@) = sin ((60^(@) + delta _(m))/(2))`
`45^(@) xx 2 = 60^(@) + delta_(m) therefore delta_(m) = 30^(@)`
and `i = (A + delta_(m))/(2) = (60^(@) + 30^(@))/(2) = 45^(@)`
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