A thin prism with angle 4° made of glass having refractive index 1.54, is combined with another thin prism made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism in degree is [2025]

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Solution

Q.
A thin prism $P_{1}$ with angle 4° made of glass having refractive index 1.54, is combined with another thin prism $P_{2}$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $P_{2}$ in degree is [2025]

1 4

2 3

3 16/3

4 1.5

Ans.
(2)

For dispersion without deviation, $δ_{net} = 0$

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

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

or $A_{2} = \frac{0.54}{0.72} \times 4 = 3 °$

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