question_answer

If tube length of astronomical telescope is 105 cm and magnifying power is 20 for normal setting. The focal length of objective is

A)  100cm                                 

B)  10cm

C)  20cm                                   

D)  25cm

Correct Answer: A

Solution :

                 To see with relaxed eye, final image should be formed at infinity. The length of telescope is given by                 \[L={{f}_{0}}+{{f}_{e}}\]                                ... (i)                 and magnifying power                  \[M=\frac{{{f}_{o}}}{{{f}_{e}}}\]                               ... (ii) Given,   L = 105,                 M = 20 \[\therefore \]  \[{{f}_{0}}+{{f}_{e}}=105\]                           ... (iii)                 \[\frac{{{f}_{o}}}{{{f}_{e}}}=20\]                               ... (iv) From Eqs. (iii) and (iv), we get                 \[20\,\,{{f}_{e}}+{{f}_{e}}=105\] \[\Rightarrow \]               \[21{{f}_{e}}=105\] \[\Rightarrow \]               \[{{f}_{e}}=\frac{105}{21}=5\,cm\] \[\Rightarrow \]               \[{{f}_{o}}=105-5=100\,\,cm\]