A thin prism $P_{1}$ of angle $4 °$ and made from glass refractive index 1.54, is combined with another prism $P_{2}$ made from a glass with refractive in 1.72, to produce dispersion without deviation. angle of $P_{2}$ is

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$5.33 °$

$4 °$

$3 °$

$2.6 °$

answer is C.

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Detailed Solution

For combination to produce dispersion without deviation.

$(n_{1} - 1) A_{1} = (n_{2} - 1) A_{2}$

$\Rightarrow A_{2} = (\frac{n_{1} - 1}{n_{2} - 1}) A_{1} \Rightarrow A_{2} = (\frac{1.54 - 1}{1.72 - 1}) 4 ° \Rightarrow A_{2} = \frac{3}{4} (4 °) \Rightarrow A_{2} = 3 °$

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