question_answer

The focal length of the objective of a telescope is 60 cm. To obtain a magnification of 20 for the relaxed eye, the length of telescope should be

A)  80 cm                                  

B)  40 cm

C)  63 cm                                  

D)  57 cm

Correct Answer: C

Solution :

                 To see with relaxed eye, final image should be formed at infinity. Length of telescope \[L={{f}_{0}}+{{f}_{e}}\]      ... (i) and magnification\[M=\frac{{{f}_{0}}}{{{f}_{e}}}\]            ... (ii) Given, M = 20,   \[{{f}_{0}}=60\] \[\therefore \]  \[{{f}_{e}}=\frac{60}{20}=3\,cm\] \[\therefore \]  \[L={{f}_{0}}={{f}_{e}}\]                 = 60 + 3 = 63 cm