A thin prism having refracting angle `10^(@)` is made of glass of refracting index `1.42`. This prism is combined with another thin prism of glass of refractive index `1.7`. This combination produces dispersion without deviation. The refracting angle of second prism should be `:`

Options

A. `4^(@)`
B. `6^(@)`
C. `8^(@)`
D. `10^(@)`

Answer

B

Explanation

For a thin prism of refracting angle A and refractive index `mu`, the angle of deviation is given by:
`delta = (mu- 1)A`
Let the refracting angle of the second prism be A.. For the given condition of zero deviation:
`(mu-1)A+(mu.-1)A.=0`
Thus, the deviations produced by each of the prisms is equal and opposite to other. Thus,
`|(mu-1)A|=|(mu.-1)A.|`
Or,
`(1.42-1)xx10^(@)=(1.7-1)A.`
`4.2=0.7A.`
`A.=6^(@)`