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The 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
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Verified Answer
The correct answer is:
1.72
Given for prism $\mathrm{P}_{1}$
$$
\mu=1.54,A=4^{\circ}
$$
For prism $\mathrm{P}_{2}$
$$
\mu^{\prime}=?, A^{\prime}=3^{\circ}
$$
For no deviation $=\delta +\delta ^{\prime}=0$
$\Rightarrow \quad(\mu-1) A=\left(\mu^{\prime}-1\right) A^{\prime}$
$\Rightarrow \quad(1.54-1) 4=\left(\mu^{\prime}-1\right) 3$
On solving we get $\mu^{\prime}=1.72$
$$
\mu=1.54,A=4^{\circ}
$$
For prism $\mathrm{P}_{2}$
$$
\mu^{\prime}=?, A^{\prime}=3^{\circ}
$$
For no deviation $=\delta +\delta ^{\prime}=0$
$\Rightarrow \quad(\mu-1) A=\left(\mu^{\prime}-1\right) A^{\prime}$
$\Rightarrow \quad(1.54-1) 4=\left(\mu^{\prime}-1\right) 3$
On solving we get $\mu^{\prime}=1.72$
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