Question

Question: A reflecting telescope (Fig. E34.63) is to be made by using a spherical mirror with a radius of curvature of 1.30 m and an eyepiece with a focal length of 1.10 cm. The final image is at infinity. (a) What should the distance between the eyepiece and the mirror vertex be if the object is taken to be at infinity? (b) What will the angular magnification be?

Short answer

1. The distance between the eyepiece and mirror vertex is 0.661 m.
2. The angular magnification is 59.1.

Step-by-step solution

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.

$M=\frac{f_1}{f_2}$

Calculate the distance between the eyepiece and mirror vertex

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

$d=f_1+f_2$

Now,

$$\begin{gathered} f_1=\frac{R}{2} \\ =\frac{1.30m}{2} \\ =0.65m \end{gathered}$$

And $f_2=1.10cm$

So,

$$\begin{gathered} d=f_1+f_2 \\ =0.650m+0.011m \\ =0.661m \end{gathered}$$

Calculate angular magnification

$$\begin{gathered} M=\frac{f_1}{f_2} \\ =\frac{0.650m}{0.011m} \\ =59.1 \end{gathered}$$

Thus, the distance between the eyepiece and mirror vertex is 0.661m and the angular magnification is 59.1.