Q62E - University Physics with Modern Physics

Question

The eyepiece of a refracting telescope (see Fig. 34.53) has a focal length of 9.00 cm. The distance between objective and eyepiece is 1.20 m, and the final image is at infinity. What is the angular magnification of the telescope?

Step-by-Step Solution

Answer

The angular magnification of the telescope is -12.33.

Step 1: Definition of angular magnification of the telescope

The angular magnification of the telescope is the ratio between focal length of the object and focal length of the eyepiece.

                                                 $\mathrm{M}=-\frac{{\mathrm{f}}_1}{{\mathrm{f}}_2}$

Step 2: Calculation of angular magnification of the telescope

The summation of both focal lengths equals the distance between objective and eyepiece. 

 $$\begin{gathered} s=f_1+f_2 \\ \Rightarrow f_1=s-f_2 \end{gathered}$$

 

Now, 

$$\begin{gathered} M=-\frac{f_1}{f_2} \\ =-\frac{s-f_1}{f_2} \\ =\frac{1.2m-0.09m}{0.09m} \\ =-12.33 \end{gathered}$$ 

Thus, the angular magnification of the telescope is -12.33.