Question

The Galilean Telescope. The following figure is a diagram of a Galilean telescope, or opera glass, with both the object and its final image at infinity. The image I serves as a virtual object for the eyepiece. The final image is virtual and erect (Figure 1)

 

Part A Find the angular magnification M.

 

Part B A Galilean telescope is constructed from two lenses. the 95.0-cm lens being used as the objective. What focal length should the eyepiece have if this telescope is to have the magnitude of angular magnification 6.33? Express your answer with the appropriate units.

 

Part C A telescope is constructed from two lenses, the 95.0-cm lens being used as the objective. Both the object being viewed and the final image are at infinity. Compare the lengths of this and Galilean telescopes.

Answer 1

(a)

From the figure,

$$ u=\frac{y}{\left|f_{1}\right|} \text { and } u^{\prime}=\frac{y}{\left|f_{2}\right|} $$

The angular magnification is defined as the ratio of image distance to the object. \(M=\frac{u^{\prime}}{u}=-\frac{f_{1}}{f_{2}}\)

The negative sign for a convex lens, because it inverts the image.

(b)

Calculate the focal length as follows:

\(f_{2}=-\frac{f_{1}}{M}=-\frac{95 \mathrm{~cm}}{6.33}=-15 \mathrm{~cm}\)

(c)

For Galilean telescope, \(L_{0}=f_{1}-f_{2}\)

For astronomical telescope, \(L=f_{1}+f_{2}\)

Compare the telescopes as follows:

\(\frac{L}{L_{0}}=\frac{f_{1}+f_{2}}{f_{1}-f_{2}}=\frac{95 \mathrm{~cm}+15 \mathrm{~cm}}{95 \mathrm{~cm}-15 \mathrm{~cm}}=\frac{110 \mathrm{~cm}}{80 \mathrm{~cm}}=1.38\)