A simple telescope is used for astrophotography (taking pictures of the stars).

Question

A simple telescope is used for astrophotography (taking pictures of the stars). The stars are (of course) at a great distance. The diameter of the entrance lens of the camera is d. A student says, "We should put the camera plane at a distance from the lens that equals the focal length, f." Is the student right or wrong? Explain. The ratio of angular size in the sky over the physical distance in the camera plane is called the "plate scale". What is the plate scale for this system in terms of f and/or d? Suppose after taking photographs of the stars you decide to use the same telescope camera system to take a photo of a deer which is located at a finite distance D from your camera. The effect of focusing changes the distance between the lens and the camera plane. By how much and in what direction must you change the lens-to-camera plane distance so that the image of the deer is sharply focused on the film?

Explanation / Answer

As we see the lens equation says

1/v +1/u=1/f

since u is infinity

1/v=1/f

so v=f

so yes camera should be kept at focal length

part B

plate scale=d/f

Part C

if u=D

we got

1/D+1/u=1/f

we got

1/v=1/f-1/D=D-f/Df

we got v=Df/(D-f)

so difference=f-Df/(D-f)=Df-f^2-Df/(D-f)=-f^2/(D-f)

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