question_answer

Draw a labelled ray diagram of an astronomical telescope, forming the image at infinity.

An astronomical telescope uses two lenses of powers 10D and 1D.

(i) State with reason, which lens is preferred of objective and eyepiece.

(ii) Calculate the magnifying power of the telescope, if the final image is formed at the near point.

Answer:

Diagram of Astronomical Telescope Ray diagram of astronomical telescope Given, power \[{{P}_{1}}=10\,D\] and \[{{P}_{2}}=1\,D\] (i) To get larger magnification, \[{{f}_{o}}\] must be large and \[{{f}_{e}}\] must be small as \[m=-{{f}_{o}}/{{f}_{e}}\] As,        \[P=\frac{1}{f}\] Lens of power 10 dioptre is suitable for eyepiece and that of power 1 dioptre is suitable for objective. (ii) Focal length of eyepiece, \[{{f}_{e}}=\frac{100}{10}=10\,cm\] Focal length of objective, \[{{f}_{o}}=\frac{100}{1}=100\,cm\] Magnifying power of the telescope, \[m=-\frac{{{f}_{o}}}{{{f}_{e}}}\left( 1+\frac{{{f}_{e}}}{D} \right)=-\frac{100}{10}\left( 1+\frac{10}{25} \right)=-14\]