Question

Magnifying power of a simple microscope is ( when final image is formed at $D=25cm$ from eye )

• A. $\frac{D}{F}$
• B. $1+\frac{D}{f}$
• C. $1+\frac{f}{D}$
• D. $1-\frac{D}{f}$

Answer 1

The correct option is B $1+\frac{D}{f}$

A Simple Microscope uses Convex lens for magnification. When the object is placed inside the focal point($f$) of the lens, then virtual ,erect and magnified image is formed at near point ($D$ = 25 cm) from the eye.
The linear magnification $m$, for the image formed at the near point $D$, by a simple microscope can be obtained by using the relation : $m=\frac{v}{u}$ , where $v$ is the image distance,$u$ is the object distance from the lens.
Using Lens Formula,$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$
$m=v(\frac{1}{v}-\frac{1}{f})=1-\frac{v}{f}$
According to Sign Convetion, $v$ is negative (image is formed at the left side of the lens instead of right side) and equal to $D$
$m=1+\frac{D}{f}$
So Magnifying Power is given by $1+\frac{D}{f}$