Choose the correct formula for magnifying power of a simple microscop…

The correct answer is Option (2) → \( m=1+\frac{d}{f} \)

A simple microscope is a convex lens with the object placed inside its focal length. Here \( d \) stands for the least distance of distinct vision (about 25 cm), and the magnifying power is greatest when the image is formed at this distance.

Using the lens formula with \( v = -d \) and the magnification \( m = v/u \):

    \( \displaystyle \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \;\Rightarrow\; \frac{v}{u} = 1 - \frac{v}{f} \)

    \( \displaystyle m = 1 - \frac{(-d)}{f} = 1 + \frac{d}{f} \)

The magnifying power is more than 1 and increases as the focal length decreases.

NCERT (2026-27):
The Microscope – “… The linear magnification m, for the image formed at the near point D, by a simple microscope can be obtained by using the relation

    \( \displaystyle m = \frac{v}{u} = v\left(\frac{1}{v} - \frac{1}{f}\right) = \left(1 - \frac{v}{f}\right) \)

Now according to our sign convention, v is negative, and is equal in magnitude to D. Thus, the magnification is

    \( \displaystyle m = \left(1 + \frac{D}{f}\right) \qquad (9.39) \)”