JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Wave Optics

Some distance star is to be observed by some telescope of diameter of objective lens a , at an angular resolution of

3.0 \times 1 0^{- 7}

radian. If the wavelength of light from the star reaching the telescope is 500 nm , the minimum diameter of the objective lens of the telescope is ______ cm. (Nearest integer)

Answer: 203

Solution

The diffraction-limited angular resolution of a telescope is

θ = \frac{1.22 λ}{D}

, so the minimum objective diameter is

D = \frac{1.22 λ}{θ} = \frac{1.22 \times 500 \times 1 0 ^{- 9}}{3.0 \times 1 0 ^{- 7}} = 2.03 m

. Converting to centimetres,

D \approx 203 cm

. The minimum diameter of the objective lens is

203 cm

JEE Main · 2026 · 08 Apr 2026 · Shift 2 · Integer answer

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