Question

The least distance of distinct vision is 25 cm If the focal length of a convex lens is 10 cm, it acts as a simple microscope with a maximum magnification of
A. 2.5
B. 3
C. 3.5
D. 5

Answer 1

Hint: As we all know that a good quality optical device is that which is having a clear image with proper resolution. The magnification parameter plays an important role in it. We define magnification as the ratio of the size of the image to the size of the object.

Complete step by step solution:
Given: The least distance of distinct vision $D = 25\,cm$.
The focal length of the convex lens is $f = 10cm$.
So we are aware that for a simple microscope, the magnification m is given by the formula:
$m = 1 + \dfrac{D}{f}$
Here m is the magnification, D is the least distance of distinct vision and $f$ is the focal length.
Now we can substitute D=25cm, f=10cm to find the value of magnification m.
$ \Rightarrow m = 1 + \dfrac{{25}}{{10}}$
$ \Rightarrow m = 1 + 2.5$
$ \Rightarrow m = 3.5$

$\therefore$The maximum magnification is 3.5. Hence, the correct option is (C).

Additional information:
The object is always placed in front of the convex mirror hence the sign of the object distance is taken as negative. In the case of a convex mirror, the image always formed behind the mirror, thus the distance of the image is taken as positive.

Note:
A convex mirror is a part of a hollow sphere having an inner part (depressed surface) silvered and the outer surface (bulging surface) as a reflecting surface. A convex mirror diverges the parallel beam of light, so they are called a diverging mirror. This mirror is also known as the driver’s mirror because it is used as the rearview mirror. The convex mirror always produces a virtual image behind the mirror which is erect, diminished. Always remember the mirror formula is the same for a concave and convex mirror.