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The plate scale of a telescope connects the angular separation of an object with the linear separation of its image at the focal plane.

If focal length ${\displaystyle f}$ is measured in mm, the plate scale in radians per mm is given by angular separation θ and the linear separation of the image at the focal plane s, or by simply the focal length f:

${\displaystyle p={\frac {\theta }{s}}={\frac {1}{f}}\ ,}$

since

${\displaystyle s=f\theta \ .}$

Plate scale is usually expressed in arcseconds per mm:

${\displaystyle p\approx {\frac {206265}{f}},}$

where f is in mm, or expressed in arcseconds per pixel after further division through the pixel scale. Plate scale is not changed when telescopes zoom in or out because the same amount of sky will be in the pixel whether it is enlarged or shrunk.

Plate scale on JWST FGS/NIRISS

The plate scale of the James Webb Space Telescope component Fine Guidance Sensor and Near Infrared Imager and Slitless Spectrograph is about 0.066 arcsec/pixel. It uses a 2040 x 2040 pixel array with a pixel size of 18 microns per side with a field of view of 2.2' x 2.2'

See also

• Photographic plate

Notes

1. Carroll, Bradley; Ostlie, Dale. An Introduction to Modern Astrophysics (1st ed.). p. 163.
2. https://jwst-docs.stsci.edu/jwst-near-infrared-imager-and-slitless-spectrograph#JWSTNearInfraredImagerandSlitlessSpectrograph-Observationalcapabilities
3. https://jwst-docs.stsci.edu/jwst-near-infrared-imager-and-slitless-spectrograph#JWSTNearInfraredImagerandSlitlessSpectrograph-Opticalelements

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