JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Geometrical Optics

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Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star.

(A) $457.5 \times 1 0^{- 9}$ radian
(B) $610 \times 1 0^{- 9}$ radian
(C) $305 \times 1 0^{- 9}$ radian✓ Correct
(D) $152.5 \times 1 0^{- 9}$ radian

Answer: (C)

Solution

The finest angle a telescope can resolve is set by diffraction at its objective, the Rayleigh criterion

θ = \frac{1.22 λ}{D}

. With

λ = 500 \times 1 0^{- 9} m

and

D = 200 cm = 2 m

θ = \frac{1.22 \times 500 \times 1 0 ^{- 9}}{2} = \frac{610 \times 1 0 ^{- 9}}{2} = 305 \times 1 0^{- 9} radian

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Single correct option

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