A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure). n1 and n2 depend on λ, the wavelength of light, according to the relation n₁ = 1.2 + 10.8 × 10⁻¹⁴λ² and n₂ = 1.45 + 1.8 × 10⁻¹⁴λ² The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _____________ nm. Numerical answer type. Work it out, then open the answer.

Answer: 600. No bending at BC for any angle of incidence requires n₁ = n₂. 1.2 + 10.8 × 10⁻¹⁴λ² = 1.45 + 1.8 × 10⁻¹⁴λ² 9 × 10⁻¹⁴λ² = 0.25 ⇒ λ² = 36 × 10⁻¹⁴ m² λ = 6 × 10⁻⁷ m = 600 nm

A prism of refractive index n1 and another prism of refractive index… | JEE Main 2021 (27 Jul, Shift 1)

Q66JEE Main 2021 · 27 JUL · SHIFT 1Difficult

Prism, Dispersion & Scattering

A prism of refractive index n1 and another prism of refractive index n2 are stuck together (as shown in the figure). n1 and n2 depend on $\lambda$ , the wavelength of light, according to the relation $n_1 = 1.2 + \frac{10.8 \times 10^{-14}}{\lambda^2}$ and $n_2 = 1.45 + \frac{1.8 \times 10^{-14}}{\lambda^2}$

The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be _____________ nm.

Numerical answer type. Work it out, then open the answer.

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Answer: 600

No bending at $BC$ for any angle of incidence requires $n_1 = n_2$ .
$1.2 + \dfrac{10.8 \times 10^{-14}}{\lambda^2} = 1.45 + \dfrac{1.8 \times 10^{-14}}{\lambda^2}$
$\dfrac{9 \times 10^{-14}}{\lambda^2} = 0.25 \Rightarrow \lambda^2 = 36 \times 10^{-14}\,\text{m}^2$
$\lambda = 6 \times 10^{-7}\,\text{m} = 600\,\text{nm}$

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