# Homework Help: Quick check on telescope optics calculations please

Tags:
1. May 5, 2012

### skydivephil

1. The problem statement, all variables and given/known data
A Cassegrain telescope has a 500mm diameter , a focal length of 5000mm and a central obstruction of 80mm diameter.
Calculate:
1) the magnification with a 25mm eye piece
2) the light gathering power compared to aye of 5mm in diameter
3) the angular field in the sky if the apparent angular field is 50 degrees
4) the angular and linear resolution for 550 nm light in arc seconds and micro meters

Most of this is easy but i just wanted to check I have to the conversion from angular resolution to linear resolution correct.

3. The attempt at a solution
1) mag= focal length scope/ eye piece length = 5000/25= 200
2) light gathering = (apeture of scope/apeture of eye)^2 =(500/5)^2 = 10,000
we have to subtract the central obstruction which is
(80/5)^2 = 256
so the answer is 10,000- 256 = 9744
3) angular field = apparent field /mag = 50/200 = .25
4) theta = 2.5 * 10^5 * lambda/diameter
= 2.5.10^5 * 550*10^-9*500810^-3
=2.5*10^5*1.1*10^-6
= 2.75 seconds of arc
To convert this into linear resolution in micro meters
apeture in um /206265
=500*10^3/206265 = 2.42
hence 2.42*2.75 = 6.66 um.

Last edited: May 5, 2012