question_answer

The length of an astronomical telescope adjusted for parallel light is 100 cm. If the magnification of the telescope is 19. The focal length of two lenses, i.e., objective and eye piece are:

A)  76 cm and 4 cm

B)  95 cm and 5 cm

C)  85 cm and 15 cm             

D)  82 cm and 18 cm

Correct Answer: B

Solution :

Key Idea: To see with relaxed eye final image should be formed at infinity. Distance between the two lenses is \[{{f}_{a}}+{{f}_{e}}=100\,\,cm\]                               ?(1) Also magnifying power \[M=-\frac{{{f}_{o}}}{{{f}_{e}}}=-19\] \[\Rightarrow \]               \[{{f}_{o}}=19\,\,{{f}_{e}}\]                         ?(2) From Eqs. (1) and (2), we get \[{{f}_{e}}=5\,cm,\,{{f}_{0}}=75\,cm\] Note: objective of telescope is taken large so that sufficient light is collected and a bright image is formed, while eyepiece is taken small so that whole light is collected at eyepiece, therefore\[{{f}_{0}}>>{{f}_{e}}\].