A thin prism $\mathrm{P}_{1}$ with angle $4^{\circ}$ made of glass having refractive index 1.54, is combined with another thin prism $\mathrm{P}_{2}$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $\mathrm{P}_{2}$ in degrees is

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Geometrical Optics

A thin prism

P_{1}

with angle

4^{\circ}

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 degrees is

(A)4
(B)3✓ Correct
(C) $16/3$
(D)1.5

Answer: (B)

Solution

For a thin prism, the deviation produced is

δ = (μ - 1) A

For dispersion without net deviation, the two thin prisms are combined so their deviations exactly cancel:

(μ_{1} - 1) A_{1} = (μ_{2} - 1) A_{2}

(1.54 - 1) (4^{\circ}) = (1.72 - 1) A_{2}

0.54 \times 4 = 0.72 A_{2} ⟹ A_{2} = \frac{2.16}{0.72} = 3^{\circ}

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Single correct option

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