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A thin prism \(p_{1}\) with angle \(4^{\circ}\) and made from glass of refractive index \(1.54\) is combined with another prism \(p_{2}\) made from glass of refractive index \(1.92\) to produce dispersion without deviation. Then the angle of prism \(P_{2}\) is
A. \(2.3^{\circ}\) B. \(4.3^{\circ} \mathrm{C} .3 .2^{\circ} \mathrm{D} .2 .0^{\circ}\)

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The angle of deviation for a prism the is given by
$$
\Delta=(n-1) \times A
$$
Where,
\(n=\) refractive index of prism
\(A=\) angle of prism
Given: The two prisms when combined produce dispersion without deviation.
Conclusion: For no deviation for the two prism the deviation caused by two prism should be opposite to each other
$$
\begin{aligned}
&\left(n_{1}-1\right) \times A_{1}=\left(n_{2}-1\right) \times A_{2} \\
&A_{2}=\frac{\left(n_{1}-1\right) \times 4}{n_{2}-1} \\
&A_{2}=\frac{(1.54-1) \times 4}{(1.92-1)} \\
&A_{2}=2.3^{\circ}
\end{aligned}
$$
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