Question

The magnifying power of a compound microscope can be increased by
A. Using both lenses of longer focal length
B. Taking objective lens of shorter focal length
C. Using both lenses of smaller focal length
D. Taking an objective lens of longer focal length and eye-lens of shorter focal length.

Answer 1

Hint: A microscope is an optical instrument which is used to see small objects like molecules of a substance or cells of an organism. Use the formula for the magnifying power as figure out what should be the condition on the focal lengths of the lenses for increasing the magnifying power.
Formula used:
$m=\dfrac{{{v}_{0}}-{{f}_{0}}}{{{f}_{0}}}\left( 1+\dfrac{D}{{{f}_{e}}} \right)$

Complete answer:
A microscope is an optical instrument which is used to see small objects like molecules of a substance or cells of an organism. A microscope magnifies the object or specimen, which helps us to see the small object more clearly and we can analyse it easily. A microscope uses lenses to magnify the object.
A compound microscope consists of two convex lenses called objective lens and eye lens.
For every microscope, we defined something called the magnifying power (m) of the microscope.
For a compound microscope, its magnifying power is given as $m=\dfrac{{{v}_{0}}-{{f}_{0}}}{{{f}_{0}}}\left( 1+\dfrac{D}{{{f}_{e}}} \right)$….. (i).
Here, ${{v}_{0}}$ is the distance of the object from the objective lens, ${{f}_{0}}$ and ${{f}_{e}}$ are the focal lengths of the objective lens and the eye lens respectively and D is the least distance of distinct vision.
From equation (i) we understand that the value of m will increase when we reduce the denominator.
This implies that the values of ${{f}_{0}}$ and ${{f}_{e}}$ must be small.
Therefore, the magnifying power of a compound microscope can be increased by using both lenses of smaller focal lengths.

Hence, the correct option is C.

Note:
Total magnification produced by a system of lenses is equal to the product of the magnifications produced by individual lenses.
The magnifying power of a compound microscope is also equal to the product of the magnification produced by the objective lens and magnification produced by the eye lens.
i.e. $m={{m}_{o}}\times {{m}_{e}}$.