A person uses + 1.5 D glasses to have normal vision from 25 cm onwards. He uses a + 20 D lens as a simple microscope to see an object. What is the maximum magnifying power if he uses the microscope without glasses.

Question

A person uses + 1.5 D glasses to have normal vision from 25 cm onwards. He uses a + 20 D lens as a simple microscope to see an object. What is the maximum magnifying power if he uses the microscope without glasses. (A) 8 (B) 9 (C) 10 (D) 11

Tardigrade Admin · Accepted Answer

Let d be the distance of near point of the person without glasses.
Focal length of glasses,

f_{1} = \frac{100}{P _{1}} = \frac{100}{1.5} = \frac{200}{3}

cm
Now u = -25 cm ; v = ?
From lens formula,

\frac{1}{v} - \frac{1}{u} = \frac{1}{f _{1}}

or

\frac{1}{v} = \frac{1}{f _{1}} + \frac{1}{u} = \frac{3}{200} - \frac{1}{25} = - \frac{5}{200}

∴ v = - \frac{200}{5} = - 40

cm
Therefore, the near point of the person is 40 cm.
Focal length of microscope,

f_{2} = \frac{100}{P _{2}} = \frac{100}{20} = 5

cm

∴ M = 1 + ∣ ∣ \frac{d}{f _{2}} ∣ ∣ = 1 + \frac{40}{5} = 9

Q. A person uses + 1.5 D glasses to have normal vision from 25 cm onwards. He uses a + 20 D lens as a simple microscope to see an object. What is the maximum magnifying power if he uses the microscope without glasses.

8

9

10

11