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, \[m=-\frac{{{f}_{o}}}{{{f}_{e}}}\left( 1+\frac{{{f}_{e}}}{D} \right)=-\frac{100}{10}\left( 1+\frac{10}{25} \right)=-14\]
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