A thin prism `P_(1)` with angle `4degree` and made from glass of refractive index 1.54 is combined with another thin prism `P_(2)` made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism `P_(2)` is

Options

A. `3^(@)`
B. `6^(@)`
C. `9^(@)`
D. `12^(@)`

Answer

A

Explanation

In case of thin prism, `delta=(mu-1)A`, when two prisms are combined together,
`delta=delta_(1)+delta_(2)=(mu-1)A+(mu.-1)A.`
For producing dispersion without deviation
`delta=0` i.e., `(mu.-1)A.=-(mu-1)A`
or `A.=-((1.54-1))/((1.72-1))xx4^(@)=-3^(@)`
So the angle of the other prism is `3^(@)` and opposite to the first.