Question

The angular magnification of an astronomical telescope in normal adjustment is 36, and the diameter of the objective lens is 72 mm. What is the minimum diameter of the eyepiece required to collect all the light entering the objective lens from a distant point source on the axis of the instrument?

Answer 1

The diameter of the lens is a simple eyepiece must be at least the diameter of the exit pupil if light entering the objective parallel to axis is not to be lost. So diameter $=\frac{72}{36}=2mm$

For $h=60+2.5f$ where h is height in cm and f is femur length.

Condition that $h>160cm$

The minimum condition for f to meet requirement for h will be,

if $h=160cm,f^{\prime }=\frac{160-60}{2.5}=40m$

With $f^{\prime }=40cm$not being a solution to this inequality,that is all values greater than 40cm will solve the inequality which is expressed as ,

$f>\frac{h-60}{2.}$