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A thin prism of angle $15^{\circ}$ made of glass of refractive index $\mu_1=1.5$ is combined with another prism of glass of refractive index $\mu_2=1.75$. The combination of the prism produces dispersion without deviation. The angle of the second prism should be
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Verified Answer
The correct answer is:
$10^{\circ}$
For without deviation
$$
\begin{aligned}
\frac{A}{A^{\prime}} & =\frac{\mu^{\prime}-1}{\mu-1} \\
\frac{15^{\circ}}{A^{\prime}} & =\frac{1.75-1}{1.5-1} \\
\frac{15}{A^{\prime}} & =\frac{0.75}{0.50} \\
A^{\prime} & =\frac{0.50 \times 15}{0.75}=10^{\circ}
\end{aligned}
$$
$$
\begin{aligned}
\frac{A}{A^{\prime}} & =\frac{\mu^{\prime}-1}{\mu-1} \\
\frac{15^{\circ}}{A^{\prime}} & =\frac{1.75-1}{1.5-1} \\
\frac{15}{A^{\prime}} & =\frac{0.75}{0.50} \\
A^{\prime} & =\frac{0.50 \times 15}{0.75}=10^{\circ}
\end{aligned}
$$
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