Find the magnification factor for the given spectrograph?

Question

For a spectrograph fed with an f/3.32 beam, and with an f/1.33 camera, what is the magnification factor of the entrance slit at the detector focal plane (larger or smaller)?

 

The question is part of chain of questions. I need to verify the answer I wrote and hence won't need long detailed steps. However do mention all the required ones 

Answer 1

Hi Anshu!

 

The information is limited, but I suspect we can use reasonable assumptions about the spectrograph to help out.

 

If we assume that (as is usually the case) that:

 

-- the light is collimated into the spectrograph; and

-- the input and output apertures are of approximately equal size

 

then the magnification factor of the entrance slit at the detector will just be the camera's f/# over the input beam's f/# (since the focal length on the camera will be the image distance of this system, and the focal length to the input collimator lens apparatus will be the object distance).  This is how the spectrometer system in my graduate project worked, and I suspect the same is true here.  However, if there is other information, please let me know.  I hope this helps!