Editing Optical telescope (section)

===Image Scale===
When using a CCD to record observations, the CCD is placed in the focal plane. Image scale (sometimes called ''plate scale'') is how the angular size of the object being observed is related to the physical size of the projected image in the focal plane

:<math>i = \frac{\alpha}{s},</math>

where <math>i</math> is the image scale, <math>\alpha</math> is the angular size of the observed object, and <math>s</math> is the physical size of the projected image. In terms of focal length image scale is

:<math>i = \frac{1}{f},</math>

where <math>i</math> is measured in radians per meter (rad/m), and <math>f</math> is measured in meters. Normally <math>i</math> is given in units of arcseconds per millimeter ("/mm). So if the focal length is measured in millimeters, the image scale is

:<math>i\ (''/\mathrm{mm}) = \frac{1}{f\ (\mathrm{mm})}\left[\frac{180 \times 3600}{\pi}\right].</math>

The derivation of this equation is fairly straightforward and the result is the same for reflecting or refracting telescopes. However, conceptually it is easier to derive by considering a reflecting telescope. If an extended object with angular size <math>\alpha</math> is observed through a telescope, then due to the [[Laws of reflection]] and [[Trigonometry]] the size of the image projected onto the focal plane will be

:<math>s = \tan(\alpha) f.</math>

The image scale (angular size of object divided by size of projected image) will be

:<math>i = \frac{\alpha}{s} = \frac{\alpha}{\tan(\alpha) f},</math>

and by using the small angle relation <math>\tan(a) \approx a</math>, when <math>a \ll 1</math> (N.B. only valid if <math>a</math> is in radians), we obtain

:<math>i = \frac{\alpha}{\alpha f} = \frac{1}{f}.</math>