A thin prism with an angle and made of glass of refractive index 1.54 is combined with another prism made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism is [2023]

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Solution

Q.
A thin prism $P_{1}$ with an angle $6 °$ and made of glass of refractive index 1.54 is combined with another prism $P_{2}$ made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism $P_{2}$ is [2023]

1 $6 °$

2 $1.3 °$

3 $7.8 °$

4 $4.5 °$

Ans.
(4)

$δ_{1} = δ_{2} [for no average deviation]$

$\Rightarrow 6 ° (1.54 - 1) = A (1.72 - 1)$

$\Rightarrow A = \frac{6 ° \times 0.54}{0.72} = \frac{18 °}{4} = 4.5 °$

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