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  4. Two glass prisms P1 and P2 are to be combined together to produce dispersion without deviation. The angles of the prisms P1 and P2 are selected as 4° and 3° respectively. If the refractive index of prism P1 is 1.54, then that of P2 will be

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Q. Two glass prisms $P_1$ and $P_2$ are to be combined together to produce dispersion without deviation. The angles of the prisms $P_1$ and $P_2$ are selected as $4^{\circ}$ and $3^{\circ}$ respectively. If the refractive index of prism $P_1$ is $1.54$, then that of $P_2$ will be

WBJEEWBJEE 2013Ray Optics and Optical Instruments

Solution:

Given for prism $P_{1}$
$\mu=1.54, A=4^{\circ}$
For prism $P_{2}$
$\mu^{\prime}=?, A^{\prime}=3^{\circ}$
For no deviation $=\delta+\delta^{\prime}=0$
$\Rightarrow (\mu-1) A=\left(\mu^{\prime}-1\right) A^{\prime}$
$\Rightarrow (1.54-1) 4=\left(\mu^{\prime}-1\right) 3$
On solving we get $\mu^{\prime}=1.72$