The angular resolution of telescope is roughly given by formula:
[tex]R= \frac{λ}{D} [/tex]
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:
[tex]R= \frac{500* 10^{-9} }{0.1524} =0.000003280839895[/tex]
Telescope B:
[tex]R= \frac{500* 10^{-9} }{0.254} =0.000001968503937[/tex]
The results are given in radians. We need to transform this into degrees.
Telescope A:
[tex]angle = 0.000003280839895 * \frac{180°}{ \pi } =0.000187978279241644°[/tex]
Telescope B:
[tex]angle = 0.000001968503937 * \frac{180°}{ \pi } =0.000112786967544986°[/tex]
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.
