Question

Telescope A has a diameter of 6 inches and a focal length of 1200mm. Telescope B has a diameter of 10 inches and a focal length of 800mm. Which telescope could distinguish two stars separated by 0.7"?

Answer 1

The angular resolution of telescope is roughly given by formula:
$R= \frac{λ}{D}$

Where:
λ = wevelength of light
D = diameter of a telescope

First step in solving this question is to convert diameter given in inches into meters:
Telescope A:
6 * 0.0254 = 0.1524m
Telescope B:
10 * 0.0254 = 0.254m

Wavelength of visible light varies from 390nm to 700nm. We will take 500nm as a number for our calculation.

Telescope A:
$R= \frac{500* 10^{-9} }{0.1524} =0.000003280839895$
Telescope B:
$R= \frac{500* 10^{-9} }{0.254} =0.000001968503937$

The results are given in radians. We need to transform this into degrees.
Telescope A:
$angle = 0.000003280839895 * \frac{180°}{ \pi } =0.000187978279241644°$
Telescope B:
$angle = 0.000001968503937 * \frac{180°}{ \pi } =0.000112786967544986°$

To find out which telescope can distinguish two stars we must convert given angle.
0.7'' is 0.7 arc seconds or 0.7 / 60 / 60 =0.0001944444444444 degrees

Telescope that has angles smaller than this can distinguish. In our case both telescopes have smaller angle and both can distinguish.