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

$\begin{array}{ccc}& ColumnI& ColumnII\\ \left(P\right)& Theprismsaremadeofsamematerialandtheirrefracting& \left(1\right)Nodeviation,Nodispersion\\ & anglesareequal,ie.,A=A^{\prime }.Thecombinationwillcause& \\ \left(Q\right)& Theprismsaremadeofsamematerialandtheirrefracting& \\ & anglesarenotequal,i.e.,A\ne A^{\prime }.Thecombinationwill& \left(2\right)Nodeviation,Dispersionhappens\\ & cause.& \\ \left(R\right)& Theprismsaremadeofdifferentmaterialandtheir& \\ & refractinganglesareequali.e.A=A^{\prime }.Alsothequantity& \\ & {\mu }_v-{\mu }_{g}hasdifferentvaluesforthetwoprisms.Here& \left(3\right)Nodispersion,deviationhappens\\ & {\mu }_{v}and{\mu }_{g}aretherefractiveindicesforvioletandred& \\ & colours.Thecombinationwillcause.& \\ \left(S\right)& Theprismsaremadeofdifferentmaterialsandtheir& \\ & refractinganglesareunequal,i.e,A\ne A^{\prime }.Also& \\ & \frac{A}{A^{\prime }}=-\frac{({\mu }^{\prime }-1)}{\mu -1},where\mu istherefractiveindexforthe& \left(4\right)Bothdeviationanddispersionhappens\\ & meanwavelength\left(yellow\right)forprismXwhile\mu isthe& \\ & correspondingvalueforprismY.Thecombinationwill& \\ & cause.& \end{array}$

• 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

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