# Focal Lengths…Usefull Formula

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Useful Formulae
Written by keith grice
Friday, 19 February 2010 01:54

The focal length of a telescope can be changed by the use of either a Barlow Lens or a Focal Reducer. You must take this into account when using the following calculations and, where appropriate,use the effective focal length. Example…the effective focal length of a 1000mm lens usede with a .63 X focal reducer will be 630mm and the same lens with a 2 X Barlow Lens will have an effective focal length of 2000mm.
Focal Ratio

Focal Ratio = Focal Length / Aperture

The result of the above will be the ” F” number of your Telescope system

Example…..A telescope with a focal length of 1000mm and an aperture of 200mm will have a focal ratio of..1000 / 200 = F5
Sampling Rates

Sampling Rate = ( 206.265 / Focal Length ) X pixel size ( in microns – um )

The result of the above will be in arcseconds / pixel

Example..The sampling rate of a camera with 7.8 um pixels used with a telescope with 600mm focal length will have a sampling rate of

( 206.265 / 600 ) X 7.8 = 2.68 arcseconds / pixel
Field Of View

FOV width = Degrees (2 * ATAN ( sensor width / ( 2* focal length )))

FOV depth = Degrees ( 2* ATAN (sensor depth / (2 * focal length )))

The result of the above will be in degrees. Multiplying the above results by 60 will convert from degrees to minutes if required.

Example..A camera with a sensor of width of 23.4mm and depth of 15.6mm used with telescope with a focal length of 480mm will capture a field of view of..

Degrees (2 X ATAN (23.4 / ( 2 X 480 )) = 2.79 degrees wide by

Degrees ( 2 X ATAN ( 15.6 / (2 X 480 )) = 1.86 degrees deep

Last Updated on Friday, 19 February 2010 01:56