Question

A simple microscope has a magnifying power of 3.0 when the image is formed at the near point (25 cm) of a normal eye. (a) What is its focal length? (b) What will be its magnifying power if the image is formed at infinity?

Answer 1

For the simple microscope, we have:
Least distance of clear vision, D = 25 cm
Magnifying power, m = 3
Now,
Let the focal length be f.

(a) When the image is formed at D = 25 cm, the magnifying power of the simple microscope is given by

m = 1 + `(D/f)`

`=> 3 =1+(25/f)`

`=> 25/f = 2`

`=> f = 25/2 = 12.5  "cm"`

(b) When the image is formed at infinity in normal adjustment, the magnifying power is given by

`m = D/f = 25/12.5 =2.0`

So, the magnifying power is 2 if the image is formed at infinity.