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Physics Question on Ray optics and optical instruments

Limit of resolution of a telescope is 4.88×10−64.88 \times 10^{-6} rad for light of wavelength 560 nm. Diameter of the objective is

A

0.14 m

B

1.4 m

C

0.07 m

D

0.7 m

Answer

0.14 m

Explanation

Solution

Here, d theta=4.88×10−6d\, theta = 4.88 \times 10^{-6}, rad,
λ=560 nm=560×10−9 m\lambda = 560 \: nm= 560 \times 10^{-9} \: m
Now, 1dθ=D1.22λ \frac{1}{d \theta} = \frac{D}{1.22 \lambda} where D is the diameter of objective.
D=1.22λdθ=1.22×560×10−94.88×10−6D = \frac{1.22 \lambda}{d\theta} = \frac{1.22 \times560\times 10^{-9}}{4.88 \times 10^{-6}}
       =140×10−3m=0.14m\, \, \, \, \, \, \, = 140 \times 10^{-3} m = 0.14 m