The aperture diameter of a telescope is 5 m. The separation between the moon and the earth is $4 \times 10^{5} \text{ km}$. With light of wavelength of 5500 Å, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to:

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Wave Optics

The aperture diameter of a telescope is 5 m. The separation between the moon and the earth is

4 \times 1 0^{5} km

. With light of wavelength of 5500 Å, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to:

(A)200 m
(B)600 m
(C)60 m✓ Correct
(D)20 m

Answer: (C)

Solution

Rayleigh's criterion sets the smallest resolvable angle at

θ = 1.22 \frac{λ}{D}

, with

λ = 5500

Å and

D = 5

m. The matching separation on the Moon is

d = θ \times r = 1.22 \times \frac{5500 \times 1 0 ^{- 10}}{5} \times 4 \times 1 0^{8} \approx 54

m, which is closest to

60

JEE Main · 2020 · 09 Jan 2020 · Shift 1 · Single correct option

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