Two stars that are very close may appear to be one. The ability of a telescope to separate their images is called its resolution. The smaller the resolution, the better a telescope's ability to separate images in the sky. In a refracting telescope, resolution θ (see the figure) can be improved by using a lens with a larger diameter D. The relationship between θ in degrees and D in meters is given by sin θ = 1.22λ/D, where λ is the wavelength of light in meters. The largest refracting telescope in the world is at the University of Chicago. At a wavelength of λ = 550 × 10−9 meter, its resolution is approximately 0.00003754°. Approximate the diameter of the lens. (Round your answer to two decimal places.)
The Attempt at a Solution
When I do it set up this way, I get a decimal, which cannot be the size of largest telescope lens.
If I divide like this: sin(.00003754)/1.22(550x10^-9) = 55.9463m this was not right.
I googled the actual telescope lens diameter and it is about 40 ft. (or 12.192m)