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?
For the simple microscope, we have:
Least distance of clear vision, D = 25 cm
Magnifying power, m = 3
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.
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