Spherical Aberration Estimation

[Parmenides]

Homework Statement

Estimate the size of the spherical abberation of a spherical mirror of 1m-diameter and a focal
length of 2 meter. (Hint: Calculate the size of the smeared image of a star at the focal point and compare it to the size (in arc-sec) of an extended object)

Homework Equations

The mirror equation $$\frac{1}{d_O} + \frac{1}{d_i} = \frac{1}{f}$$
And for large object distances, $$a = -\frac{h^4}{8}\Big[\frac{n}{d_i}\big(\frac{1}{d_i} - \frac{1}{R}\big)^2\Big]$$

The Attempt at a Solution

I don't understand how I'm given all the needed information on the basis of this question. True, the hint suggests that I have an infinite object distance, from which the mirror equation tells me the image distance is merely the focal length, $d_i = 2m$. But the $a$ for the aberration requires an aperture height $h$ and an index of refraction. Am I also to assume $n$ is 1.0 for a vacuum and then use geometry to choose some height? What does obtaining the size of an extended object have anything to do with it? Why arc seconds? I could use some additional guidance.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?