Optics Ques 6

  1. Calculate the limit of resolution of a telescope objective having a diameter of $200 \mathrm{~cm}$, if it has to detect light of wavelength $500 \mathrm{~nm}$ coming from a star.

(2019 Main, 8 April II)

(a) $610 \times 10^{-9} \mathrm{rad}$

(b) $305 \times 10^{-9} \mathrm{rad}$

(c) $457.5 \times 10^{-9} \mathrm{rad}$

(d) $152.5 \times 10^{-9} \mathrm{rad}$

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Answer:

Correct Answer: 6.( b )

Solution:

Formula:

Astronomical Telescope:

3 For a telescope, limit of resolution is given by $\Delta \theta=\frac{1.22 \lambda}{D}$

Here, $\lambda=500 \mathrm{~nm}=500 \times 10^{-9} \mathrm{~m}$,

$ D=200 \mathrm{~cm}=200 \times 10^{-2} \mathrm{~m} $

So, limit of resolution is $\Delta \theta=\frac{1.22 \times 500 \times 10^{-9}}{200 \times 10^{-2}}$

$=305 \times 10^{-9} \mathrm{rad}$



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