Astronomy 3520: Grating Review Sheet

For a reflection grating, nλ = d(sin α ± sin β), where α and β are the incident and reflected angles respectively

For a transmission grating, however, nλ = d sin θ because we assume the incident angle is 0.

To derive the resolution of a telescope, we start with the dispersion equation nλ = d sin θ

We also know that dθ = where x is the size of the image on your focal plane (in general, you probably want your smallest resolution element to be nyquist sampled, so x should be twice the pixel size) and is the focal length of your camera optics.  This can be recovered from our familiar diagram:

where in this case, the size on the focal plane is x, the focal length is the camera focal length, and θ is dθ

In the calculations below, all units will be centimeters

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What if we had been given a different value?  Say we knew the central wavelength λ = 4400 Å instead of the angle θ :

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So the resolution is higher (3000), but our camera has to be at an angle of 45 degrees instead of 35 degrees for the first order

Created by Wolfram Mathematica 6.0  (08 November 2007)