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Question:
A person uses 1.5D glasses to have normal vision from 25 cm onwards. He uses a 20D lens as a simple microscope to see an object. What is the maximum magnifying power if he used the microscope together with his glasses as well as without the glasses?
Answer:

The person uses +1.5 D glasses to have normal vision at 25 cm.

So, with glasses his least distance of clear vision, D=25 cm

Focal length of glasses = 1/1.5 m = 100/1.5 cm

So, without the glasses his least distance of distinct vision should be more-

If u= -25 cm, f = 100/1.5 cm

Now, 1/v -1/u = 1/f

= 1.5/100 -1/25 = -2.5/100

Near point without glasses, v = -40 cm

Focal length f of microscope = 1/20 m =0.05 m = 5 cm

Hence,

1. The maximum magnifying power with glasses-

m = 1+(D/f)  = 1+(25/5) = 6                (D= 25 cm)

2. The maximum magnifying power without glasses-

m = 1+(D/f)  = 1+(40/5) = 9            (D= 40 cm)

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