Question

Four lenses having the local length of +15 cm, 20 cm, +150 cm, and +250 cm respectively are provided to make a astronomical telescope. The focal length of the eyepiece to produce the largest magnification, should be :

• A. +250 cm
• B. +155 cm
• C. 25 cm
• D. +15 cm

Answer 1

Answer: (D)

+15 cm

For a compound microscope, magnification is given by $m=\frac{f_o}{f_e}(1+\frac{f_e}{D})$

$⟹$ $m=\frac{f_o}{f_e}+\frac{f_o}{D}$
Thus, $m$ is inversely proportional to the focal length of the eyepiece $f_e$.

Thus, smaller the focal length of the eyepiece, larger is the magnification.
Hence, $f_e=15cm$ is the perfect choice.