# Spherical Aberration Estimation

1. Oct 4, 2014

### Parmenides

1. The problem statement, all variables and given/known data
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)

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

3. 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.

2. Oct 9, 2014