Question

A $20x$telescope has a $12cm$diameter objective lens. What minimum diameter must the eyepiece lens have to collect all the light rays from an on-axis distant source?

Short answer

The minimum diameter is$6mm$.

Step-by-step solution

Given Information.

We have given that:

Magnification is$M=20$,

Objective lens = $12cm$diameter.

We need to find what minimum diameter must the eyepiece lens have to collect all the light rays from an on-axis distant source.

Simplification.

Firstly, we need to find the focal length of eyepiece $f_{eye}$

As we know

$M=20$

localid="1648754018228" $f_{obj}=\frac{12cm}{2}=6cm.$

Since,

$M=\frac{f_{obj}}{f_{eye}}$

$f_{eye}=\frac{f_{obj}}{M}$

$f_{eye}=\frac{6cm}{20}$

$f_{eye}=0.3cm$

Therefore the diameter D of the eyepiece:

$D=2\times 0.3cm$

localid="1648632623279" $=0.6cm\to 6mm$

Here $D$is the diameter, $f_{eye}$is the focal length of i, $f_{obj}$is the focal length of the object,$M$is a magnification.