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Physics Question on Ray optics and optical instruments

Assume that light of wavelength 600 nm600\, nm is coming from a star. The limit of resolution of telescope whose objective has a diameter of 2 m2\,m is :

A

3.66×10−7 rad3.66 \times 10^{-7} \,rad

B

1.83×10−7 rad1.83 \times 10^{-7} \,rad

C

7.32×10−7 rad7.32 \times 10^{-7} \,rad

D

6.00×10−7 rad6.00 \times 10^{-7} \,rad

Answer

3.66×10−7 rad3.66 \times 10^{-7} \,rad

Explanation

Solution

Limit of resolution,
θR=1.22λd\theta_{R}=1.22 \frac{\lambda}{d};
λ=600×10−9 m\lambda=600 \times 10^{-9}\,m
d=2 md=2\,m
θR=1.22×600×10−92\theta_{R}=\frac{1.22 \times 600 \times 10^{-9}}{2}
θR=3.66×10−7\theta_{R}=3.66 \times 10^{-7} rad