# A Compound Microscope Has a Magnifying Power of 100 When the Image is Formed at Infinity. - Physics

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 eyepiece.

#### Solution

For the compound microscope, we have:
Magnifying power, m = 100

Focal length of the objective, f0 = 0.5 cm  Tube length,   l = 6.5 cm

Since the image is formed at infinity, the real image produced by the objective lens should lie on the focus of the eyepiece.

∴ vo + fe = 6.5 cm  .....(1)

The magnifying power for normal adjustment is given by

m = v_0/u_0 × D/f_e

=-[1-v_0/f_0]D/f_e

=> 100 = -[1-v_0/0.5] × 25/f_e

⇒ 2vo -4fe = 1 ..(2)

On solving equations (1) and (2), we get:

v0 =4.5 cm and fe =2 cm

Thus, the focal length of the eyepiece is 2 cm.

Concept: Magnification
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#### APPEARS IN

HC Verma Class 11, 12 Concepts of Physics 1
Chapter 19 Optical Instruments
Q 9 | Page 432