Question

the hubble space telescope has an objective diameter of 2.4 m. suppose it is viewing the mars from a distance of 80 million km away.

estimate the minimum size of an object on mars (in km) that can be distinguished by the hubble when using a wavelength of 490 nm

Answer 1

The angular Resolution is given by,

$\theta=1.220\frac{\lambda}{D}$

where

? is the angular resolution (radians),

? is the wavelength of light,

and D is the diameter of the lens' aperture.

So, we have,

$\theta=1.220*\frac{490*10^{-9}}{2.4}$

$\Rightarrow \theta=2.4908*10^{-7}$

Distance, R = 80 million km= 8* 10¹⁰ m

Resolving distance,

$\Delta l=R\theta$

$\Rightarrow \Delta l=8*10^{10}*2.49083*10^{-7}$

$\Rightarrow \Delta l=199267\;m\approx 19.927\;km$