Answer:
0.255 m
Explanation:
We are given that
Diameter=d=63.5 cm=[tex]63.5\times 10^{-2} m[/tex]
[tex]1 cm=10^{-2} m[/tex]
L=265 km =[tex]265\times 1000=265000 m[/tex]
Wavelength,[tex]\lambda=500nm=500\times 10^{-9} m[/tex]
[tex]1nm=10^{-9} m[/tex]
We have to find the minimum distance between two objects on the ground if their images are to be resolved by this lens.
[tex]sin\theta=1.22\frac{\lambda}{d}[/tex]
[tex]sin\theta=\frac{1.22\times 500\times 10^{-9}}{63.5\times 10^{-2}}[/tex]
[tex]sin\theta=\approx \theta=9.606\times 10^{-7} rad[/tex]
[tex]\frac{y}{L}=tan\theta\approx \theta[/tex]
[tex]y=L\theta=265000\times 9.606\times 10^{-7}=0.255 m[/tex]
