Write down maximum and minimum values of magnifying power of a simple microscope?

Question: Write down maximum and minimum values of magnifying power of a simple microscope?

In this blog post, we will learn how to write down the maximum and minimum values of magnifying power of a simple microscope. A simple microscope is a device that uses a single lens to magnify an object. The magnifying power of a simple microscope is the ratio of the angular size of the image to the angular size of the object when both are measured at the near point of the eye.

The maximum magnifying power of a simple microscope occurs when the image is formed at infinity. In this case, the object is placed at the focus of the lens and the angular size of the image is equal to the angular magnification of the lens. The angular magnification of a lens is given by:

M = 1 + D/f

where D is the least distance of distinct vision (about 25 cm for a normal eye) and f is the focal length of the lens. Therefore, the maximum magnifying power of a simple microscope is:

M_max = 1 + D/f

The minimum magnifying power of a simple microscope occurs when the image is formed at the near point of the eye. In this case, the object is placed at a distance u from the lens such that:

1/u + 1/v = 1/f

where v is the image distance and f is the focal length of the lens. The angular size of the image is then given by:

theta_i = v/D

The angular size of the object is given by:

theta_o = u/D

Therefore, the magnifying power of a simple microscope is:

M = theta_i/theta_o = v/u

Substituting v from the lens equation, we get:

M = f/(u - f)

The minimum magnifying power occurs when u is as large as possible, which means that u = D. Therefore, the minimum magnifying power of a simple microscope is:

M_min = f/(D - f)