The aperture diameter of a telescope is $$5m$$. The separation between the moon and the earth is $$4\times 10^5$$ km. With light of wavelength of $$5500\overset{o}{A}$$, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to?
Correct option is A. $$60$$ m
Refer above image.
Let the aperture $$=d$$ $$D=4\times 10^8m$$
$$wavelength =\lambda=5500\times 10^{-10}m$$
for two objects to be resolved
$$\theta=1.22\dfrac{\lambda}{d}$$
also $$d=D\theta$$
$$\Rightarrow \theta=\dfrac{d}{D}$$
$$\Rightarrow \dfrac{d}{4\times 10^8}=\dfrac{1.22\times 5500\times 10^{-10}}{5}$$
$$d=53.68\approx 60m$$
Option A is correct.