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How can the resolving power of a microscope be increased?

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Hint: The microscope is an optical device that is used to view the objects of the size of microns $\left( {{{10}^{ - 6}}m} \right)$. The ability of the microscope to view images of such small sizes is by the virtue of its high resolving power, which refers to the property of the optical device to distinguish two different sources of light separately.

Complete answer:
The resolving power is defined as the ability of an optical device or an imaging system to identify in detail the individual components that make up the whole part.
For example, if we look at a leaf through magnifying glass, we can only differentiate between the lines on it which cannot be differentiated through naked eye otherwise. Now, if we look at the same leaf through a device called a microscope, we are able to identify the structure of chlorophyll and the cell structure.
This is because we have shifted from a lens which has low resolving power compared to a microscope which has a higher resolving power.
The microscope is a device used to view objects of the size in micrometres $\left( {{{10}^{ - 6}}m} \right)$ by the virtue of its high resolving power that enables us to differentiate two objects at the distance of a micron. It consists of two lenses – objective, the lens present near the object and the eyepiece, used for viewing by the user.
The resolving power of a microscope is given by the formula –
$R = \dfrac{{2n\sin \theta }}{\lambda }$
where,
n = refractive index of the lens material used
$\theta $ = half-angle subtended by the image on the eyepiece.
$\lambda $= wavelength of the back light used to illuminate the object.
Thus, the resolving power is directly proportional to half-angle subtended, refractive index and inversely proportional to the wavelength of the light used for illumination.
The resolving power, thus defined, can be increased in the following ways:
i) Increasing the half-angle, $\sin \theta $ – This can be done by bringing the objective lens closer to the specimen.
ii) Increasing the refractive index, n – There are many ways to increase the refractive index such as varying the lens used or using oil as a medium. For example, we have oil immersion microscopes.
iii) Decreasing the wavelength of the backlight for illumination, $\lambda $
By using high frequency radiation such as X-rays or ultraviolet radiation, the resolving power can be increased.
Therefore, these are three ways in which the resolving power of a microscope can be increased.

Note: To increase the resolving power to very high values, such as studying atomic level interaction, we have to decrease the wavelength drastically. Using the highest frequency gamma rays can be very fatal. Hence, electron waves of high frequencies are used and they are called electron microscopes.