A thin prism $\mathrm{P}_{1}$ with an angle $6^{\circ}$ and made of glass of refractive index 1.54 is combined with another prism $\mathrm{P}_{2}$ made from glass of refractive index 1.72 to produce dispersion without average deviation. The angle of prism $\mathrm{P}_{2}$ is :

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Geometrical Optics

A thin prism

P_{1}

with an angle

6^{\circ}

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 :

(A) $6^{\circ}$
(B) $1. 3^{\circ}$
(C) $7. 8^{\circ}$
(D) $4. 5^{\circ}$ ✓ Correct

Answer: (D)

Solution

For a thin prism the deviation is

δ = A (μ - 1)

. Producing dispersion without net (average) deviation requires the two deviations to be equal in magnitude and opposite,

A_{1} (μ_{1} - 1) = A_{2} (μ_{2} - 1)

. Substituting

A_{1} = 6^{\circ}

μ_{1} = 1.54

and

μ_{2} = 1.72

6^{\circ} \times 0.54 = A_{2} \times 0.72

, so the angle of the second prism is

A_{2} = \frac{6 ^{\circ} \times 0.54}{0.72} = 4. 5^{\circ}

JEE Main · 2023 · 30 Jan 2023 · Shift 2 · Single correct option

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