Question

Suppose you wanted to be able to see astronauts on the moon. what is the smallest diameter of the objective lens required to resolve a 0.67 m object on the moon? assme the wavelength of the light is near the middle of the visible spectrum: 550 nm yellow light.

Answer 1

r = distance of moon from earth = 3.84 x 10⁸ m

R = size of the object on moon = 0.67 m

D = diameter of the lens = ?

`\lambda` = wavelength of light = 550 x 10⁻⁹ m

Using the equation for Rayleigh criterion

R/r = 1.22
`\lambda`/D

inserting the values

0.67/(3.84 x 10⁸) = 1.22 (550 x 10⁻⁹) /D

D = 384.6 m