Question

The objective lens of a certain refracting telescope has a diameter of 63.5 cm. The telescope is mounted in a satellite that orbits the Earth at an altitude of 265 km to view objects on the Earth's surface. Assuming an average wavelength of 500 nm, find the minimum distance between two objects on the ground if their images are to be resolved by this lens.

Answer 1

0.255 m

Step-by-step explanation:

We are given that

Diameter=d=63.5 cm=
`63.5* 10^(-2) m`

`1 cm=10^(-2) m`

L=265 km =
`265* 1000=265000 m`

Wavelength,
`\lambda=500nm=500* 10^(-9) m`

`1nm=10^(-9) m`

We have to find the minimum distance between two objects on the ground if their images are to be resolved by this lens.

`sin\theta=1.22(\lambda)/(d)`

`sin\theta=(1.22* 500* 10^(-9))/(63.5* 10^(-2))`

`sin\theta=\approx \theta=9.606* 10^(-7) rad`

`(y)/(L)=tan\theta\approx \theta`

`y=L\theta=265000* 9.606* 10^(-7)=0.255 m`