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Wave Optics question

2019 · 8 Apr · Shift 2 · Q71
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Wave Optics question

2019 · 8 Apr · Shift 2 · Q71

JEE MainPhysicsWave OpticsMCQ+4 / −1
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 :-
  1. A
    610 × 10–9 radian
  2. B
    457.5 × 10–9 radian
  3. C
    305 × 10–9 radian
  4. D
    152.5 × 10–9 radian
View written solutionFree

Correct answer: C

  1. Use Rayleigh’s criterion for a telescope

For a circular aperture, the minimum angular resolution is

θ=1.22 λD\theta = 1.22\,\frac{\lambda}{D}θ=1.22Dλ​

where:

  • λ=500 nm=500×10−9 m\lambda = 500\text{ nm} = 500 \times 10^{-9}\text{ m}λ=500 nm=500×10−9 m
  • D=200 cm=2 mD = 200\text{ cm} = 2\text{ m}D=200 cm=2 m
  1. Substitute the values
θ=1.22×500×10−92\theta = 1.22\times \frac{500\times 10^{-9}}{2}θ=1.22×2500×10−9​ θ=1.22×250×10−9\theta = 1.22\times 250\times 10^{-9}θ=1.22×250×10−9 θ=305×10−9 rad\theta = 305\times 10^{-9}\text{ rad}θ=305×10−9 rad
  1. Match with the options

The calculated value is:

305×10−9 radian\boxed{305 \times 10^{-9}\text{ radian}}305×10−9 radian​

So the correct option is C.

  1. Comparison with stored correct answer

Stored correct answer: C

My derived answer: C

They match.

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