Question

If a single-mirror optical telescope could resolve an Earth-size planet 5 light years away. Calculate the minimum size of the mirror.

Answer 1

Okay, Here we need to assume some wavelength in the visible range.

I am assuming a wavelength of 500 nm

Therefore,

To resolve the given planet, the angular resolution

= 2R / d

where R is radius of earth as we are told that planet is having size of earth

so,

= 2 * 6370 * 1000 / 5 * 9.461e15

= 2.693e-10 rad

so,

we know as per Rayleigh

= 1.22 / D

2.693e-10 = 1.22 * 500e-9 / D

so,

D = 2265 meters