A distant star is observed with a telescope. The required angular resolution is 3.0×10⁻⁷ rad and the wavelength of the received light is 500 nm. Using the Rayleigh criterion θ = 1.22λ ÷ D, find the minimum objective diameter D in centimetres, to the nearest integer.
Physics · Wave Optics · diffraction of light
JEE Mains 2026 8 April Evening Shift

Question

A distant star is observed with a telescope. The required angular resolution is 3.0×10⁻⁷ rad and the wavelength of the received light is 500 nm. Using the Rayleigh criterion θ = 1.22λ ÷ D, find the minimum objective diameter D in centimetres, to the nearest integer.

Physics · Wave Optics · diffraction of light

JEE Mains 2026 8 April Evening Shift

G1 Physics · Accepted Answer

Rayleigh's criterion is θ = 1.22λ ÷ D. Therefore, D = 1.22λ ÷ θ. Given, λ = 500 nm = 5.0×10⁻⁷ m, θ = 3.0×10⁻⁷ rad. Thus, D = 1.22×5.0×10⁻⁷ ÷ (3.0×10⁻⁷) = 1.22×5 ÷ 3 ≈ 2.033 m. Convert to centimetres: D ≈ 203.3 cm. To the nearest integer, D = 203 cm. Therefore the answer is 203.