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The least distance of distinct vision is $25cm$ . The focal length of a convex lens of a simple microscope is $5cm$ . Its magnifying power if the image is at a near point
a. $4$
b. $5$
c. $6$
d. $7$

Last updated date: 24th Jun 2024
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Hint: Good optical device is that which is requiring a clear image with proper resolution. The magnification parameter plays an important role in it. We refer to magnification as the ratio of the size of the image to the size of the object.

Complete step by step answer:
Given: The least distance of distinct vision $D = 25cm$ .
The focal length of the simple microscope $f = 5cm$ .
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 $D = 25cm$, $f = 5cm$ to find the value of magnification $m$ .
$\therefore m = 1 + \dfrac{{25}}{5}$
On further solving we get,
$m = 1 + 5$
$ \Rightarrow m = 6$

Hence, the correct answer is option (C).

Additional information:
A simple microscope is commonly used to study small samples by making its magnified view. Enlarged image of this specimen made by a biconvex lens. If the distance between the sample and lens is less, better magnification can attain. The contrast of the image can be controlled by making slight changes to the light that we are using. It can be used in various fields including microbiology applications, the study of soil, skin cells, etc.
The object is each time placed in front of the convex mirror therefore the sign of the object distance is taken as negative. In the case of a convex, the image is always made behind the mirror, thus the distance of the image is taken as positive.

Note: A convex mirror is a fragment 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, as a result, it is called a diverging mirror. This mirror is also known as the driver’s mirror because it is used as the rear-view mirror.