The magnifying power of a microscope with an objective of 5 mm focal length is 4

Question

The magnifying power of a microscope with an objective of 5 mm focal length is 400. The length of its tube is 20 cm. Then the focal length of the eye-piece is (consider that final image is formed at infinity)

Options:

A . 200 cm

B . 160 cm

C . 2.5 cm

D . 0.1 cm

Answer: Option C
:
C

m_{\infty} = \frac{(L - f_{o} - f_{e}) D}{f_{o} f_{e}} ≃ \frac{L D}{f_{o} f_{e}}

\Rightarrow 400 = \frac{20 \times 25}{0.5 \times f_{e}} \Rightarrow f_{e} = 2.5 c m .

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