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A monochromatic ray of light is incident...

A monochromatic ray of light is incident at an angle of `50^(@)` on one of the refracting surfaces of an equilateral prism . What is the refractive index of the material of the prism , if the angle of emergence is also `50^(@)` ?
[ sin `50^(@) = 0.767]`

A

`1.46`

B

`1.532`

C

`1.57`

D

`1.62`

Text Solution

Verified by Experts

The correct Answer is:
B
A = `60^(@) , i= 50^(@) and e =50^(@)`
In this case i=e
Hence the ray suffers minimum deviation.
`therefore` Using `i+ e = A + delta m`,
we get , `delta m = i+ e - A = 50^(@) + 50^(@) - 60^(@) = 40^(@)`
`therefore n = (sin ((60^(@) + 40^(@))/(2)))/(sin 30^(@)) = (sin 50^(@))/((1)/(2)) = 2 sin 50^(@)`
`therefore n = 2 xx 0.766 = 1.532`
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