Chapter 25, Problem 33P

To determine

The magnification of the Galilean telescope.

Answer to Problem 33P

Solution:

The magnification of the given Galilean telescope is found to be $+18\times$.

Explanation of Solution

Explanation;:

A Galilean telescope has convex lens which functions as its objective and a concave lens as its eye piece. The telescope produces an erect image of the object.

Angular magnification M of the telescope is the ratio of the focal lengths of the objective and the eye piece.

$M=-\frac{f_o}{f_e}$

Here, the focal length of the objective lens is $f_o$ and the focal length of the eye piece is $f_e$.

The length l of the telescope is the sum of the focal lengths of the objective and the eye piece.

$l=f_o+f_e$

Given:

The length of the telescope $l=36.8\text{ cm}$

The focal length of the objective $f_o=39.0\text{ cm}$

Formula:

$\begin{array}{l}M=-\frac{f_o}{f_e}\\ l=f_o+f_e\end{array}$

Calculation:

Using the given values of the length and the focal length of the objective, calculate the focal length of the eye piece.

$\begin{array}{c}l=f_o+f_e\\ f_e=l-f_o\\ =\left(36.8\text{ cm}\right)-\left(39.0\text{ cm}\right)\\ =-2.2\text{ cm}\end{array}$

Use the calculated value of the focal length of the eye piece $f_e$ and the value of the focal length of the objective lens $f_o$ in the expression for magnification.

$\begin{array}{c}M=-\frac{f_o}{f_e}=-\frac{\left(39.0\text{ cm}\right)}{\left(-2.2\text{ cm}\right)}\\ =+17.7\\ \approx +18\times \end{array}$