First slide

Ray optics

Question

A compound microscope has a magnifying power of 100 when the image is formed at infinity. The objective has a focal length of 0.5 cm and the tube length is 6.5 cm. Find the focal length of the eye- piece

Moderate

A

1 cm
B

2 cm
C

3 cm
D

4 cm

Solution

When final image is at infinity the magnification produced by eye piece is $\frac{D}{fe} and v_{e} = f_{e}$
$L = v_{o} + u_{e} \frac{1}{V_{o}} + \frac{1}{u_{o}} = \frac{1}{f_{o}}$
$6 .5 = V_{o} + f_{e} \frac{v_{o}}{u_{0}} + 1 = \frac{v_{o}}{f_{o}}$
$(\frac{u_{0}}{v_{o}} + 1) = \frac{(6 .5 - f_{e})}{0 .5}$
Overall magnification $\frac{v_{0}}{u_{o}} (\frac{D}{f_{e}}) = 100$
   $\frac{v_{o}}{u_{o}} = 4 f_{e}$
   $(4 f_{e} + 1) = 2 (6 .5 - f_{e})$
   $4 f_{e} + 1 = 13 - 2 f_{e}$
   $6 f_{e} = 12$
$f_{e} = 2 cm$

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