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Two stars 15 light-years away are barely resolved by a 75 cmcm (mirror diameter) telescope. 1ly=9.461×10^15...

Two stars 15 light-years away are barely resolved by a 75 cmcm (mirror diameter) telescope. 1ly=9.461×10^15 m

How far apart are the stars? Assume λλ = 550 nm and that the resolution is limited by diffraction.

Express your answer to two significant figures and include the appropriate units.

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Answer #1

This is based on Rayleigh criteria

= 1.22 / D

where D is mirror diameter

= 1.22 * 550e-9 / 0.75

= 8.946e-7 radians

The distance 'd' between two objects a distance x away and separated by an angle is d = x

so,

d = 15 * 9.461e15 * 8.946e-7

d = 1.27e11 meters

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