Question

A prism ‘X’ and another ‘Y’ are kept in contact with their refracting angles placed opposite to each other as shown in fig. White light is incident on the combination from the left. Column-I described some situation. Match Column-I with the possible out-comes given in Column-II

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{(P)}& \text{The prisms are made of same material and their refracting}& \left(1\right)& \text{No deviation, No dispersion}\\ & \text{angles are equal,i.e A=A' The combination will cause}& & \\ \text{(Q)}& \text{The prisms are made of same material and their refracting}& \left(2\right)& \text{No deviation, Dispersion happens}\\ & \text{angles are not equal,i.e}A\ne A^{\prime }.\text{The combination will}& & \\ & \text{cause}& & \\ \text{(R)}& \text{The prisms are made of different material and their}& \left(3\right)& \text{No dispersion , deviation happens}\\ & \text{refracting angles are equal i.e.A=A'.Also the quantity}& & \\ & {\mu }_v-{\mu }_g\text{has different values for the two prisms. Here}& & \\ & {\mu }_{v}and{\mu }_g\text{are the refractive indices for violet and red}& & \\ & \text{colours. The combination will cause.}& & \\ \text{(S)}& \text{The prisms are made of different materials and their}& \left(4\right)& \text{Both deviation and dispersion}\\ & \text{refracting angles are unequal,}A\ne A^{\prime }.\text{Also}& & \text{happens}\\ & \frac{A}{A^{\prime }}=-\frac{({\mu }^{\prime }-1)}{(\mu -1)},\text{where}\mu \text{is the refractive index for the}& & \\ & \text{mean wavelength (yellow) for prism X while}{\mu }^{\prime }\text{is the}& & \\ & \text{corresponding value for prism Y. The combination will}& & \\ & \text{cause}& & \end{array}$

• A. P $\to$ 2, Q $\to$ 2, R $\to$ 3, S $\to$ 1
• B. P $\to$ 3, Q $\to$ 3, R $\to$ 4, S $\to$ 1
• C. P $\to$ 1, Q $\to$ 4, R $\to$ 4, S $\to$ 2
• D. P $\to$ 4, Q $\to$ 2, R $\to$ 3, S $\to$ 1

Answer 1

The correct option is C

P $\to$ 1, Q $\to$ 4, R $\to$ 4, S $\to$ 2

$\omega =\frac{{\mu }_V-{\mu }_R}{\mu -1}$ and $d=(\mu -1)A$