How far apart are two stars resolved by a 68-cm telescope?

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Homework Statement


Two stars 18 light-years away are barely resolved by a 68 -cm (mirror diameter) telescope. How far apart are the stars? Assume \lambda = 540 <units>nm</units> and that the resolution is limited by diffraction.
Express your answer using two significant figures.



Homework Equations


Theta=(1.22 lambda)/diameter of the lense

9.4605284 × 10^15 meters


The Attempt at a Solution


I have no clue how to do this. I plugged the give info into the equation and got theta to equal 9.6882352941176470588235294117647e-7 then i just plugged this into the Pythagorean equation to get 559491313771834207552834.45286104
 
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Roughly from similair triangles:
lamba/D = separation/distance

The angle between the stars is 1.22lambda/D so you can work out this angle (remember is answer in radians) then you have the angle between two stars a distance away so getting the distance between them is easy.
Since the angles are small you can use the apprx theta = sin theta (in radians)
 
I have worked it out both ways and both of the answers i got were wrong
 
Remember, as mgb_phys stated, Rayleigh's Criterion expresses the angular distance in radians.

If you're still getting the incorrect answer I suggest you explicitly post how you're calculating the distance.
 

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