The resolution of a telescope is ultimately limited by the diameter of its objec

Question

The resolution of a telescope is ultimately limited by the diameter of its objective lens or mirror. A typical amateur astronomer's telescope may have a 7.0in. -diameter mirror.

What is the minimum distance (in km) between two points on the Moon's surface that can be resolved by a 7.0in. . scope? (Note: The average distance from Earth to the Moon is 384,400 km.) y=______ km

The resolution of a telescope is ultimately limited by the diameter of its objective lens or mirror. A typical amateur astronomer's telescope may have a 7.0in. -diameter mirror. What is the minimum angular separation (in arc seconds) of two stars that can be resolved with a 7.0in. scope? (Take ? to be at the center of the visible spectrum, about 550 nm, and note that 1 arc sec = 1/3600 ?) Theta min= arc seconds. What is the minimum distance (in km) between two points on the Moon's surface that can be resolved by a 7.0in. . scope? (Note: The average distance from Earth to the Moon is 384,400 km.) y= km

Explanation / Answer

Diameter of the mirror d = 7.0 in
= 7.0 * 2.54 cm
= 7.0 * 2.54 / 100 m
= 0.178 m
wavelength ? = 550 * 10 ^ -9 m
The minimum angular separation ? = 1.22 ? /d
= 3.77 * 10 ^ -6 rad
we know 1 rad = 206264.806247 arc seconds
So, The minimum angular separation ? = 3.77* 10^ -6 * 206264.806247 arc seconds
= 0.777 arc seconds
(B ) Minimum distance = 1.22 ?D / d
= 3.77* 10 ^ -6 * 384400000 m
= 1449.19 m

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