Find Telescope Diameter to Resolve Two Stars

[dimensionless]

I have two stars that are separated by an angle of 3x10^5 radians. They are both emitting monochromatic light on 600nm. I would like to find the diameter of the smallest telescope that can resolve the two stars.

For the angular limit of resolution I have
<br /> \Delta \theta = \frac{1.22 \lambda}{D}<br />

Where D is the diameter of the lens.

Rearranging I get
<br /> D = \frac{1.22 \lambda}{\Delta\theta}=\frac{1.22*600*10^{-9}}{3*10^{-5}} = 2.44 cm<br />

I'm quite sure that the answer is 2.5 cm. Where am I going wrong? Where does the 1.22 come from?

 

[Doc Al]

I'm quite sure that the answer is 2.5 cm. Where am I going wrong?

I don't think you're going wrong at all.

Where does the 1.22 come from?

The resolution limit you are using is called Rayleigh's criteria. The 1.22 comes from calculating the diameter of the first dark ring of the Fraunhofer diffraction pattern due to a circular aperature (which involves finding the zeros of a Bessel function--look it up if you want more).