Write for the formula for resolution of microscope and explain the symbols used.

The resolution of a microscope refers to its ability to distinguish and separate two closely spaced objects as distinct entities. In other words, it is a measure of how much fine detail the microscope can reveal in an image. The formula for resolution is given by:

Resolution = λ / (2 * NA)

Where:

Resolution: This represents the minimum resolvable distance, commonly denoted in units like nanometers (nm) or micrometers (μm). It signifies the smallest separation between two points that can be distinguished by the microscope.
λ (Lambda): This symbolizes the wavelength of the light used in the imaging process. In optical microscopy, visible light is typically used, and its wavelength is in the range of 400 nm (violet) to 700 nm (red).
NA (Numerical Aperture): This is a dimensionless quantity that characterizes the light-gathering ability of the microscope's objective lens. It accounts for the angle of light rays accepted by the lens and the refractive index of the medium between the lens and the specimen. The higher the NA, the greater the resolving power of the microscope.
To explain the formula, let's see how wavelength and numerical aperture impact the resolution:

Wavelength (λ): The resolution is inversely proportional to the wavelength. This means that as the wavelength decreases, the resolution improves. In other words, shorter wavelengths can reveal finer details. This is why electron microscopes, which use much shorter electron wavelengths, can achieve higher resolution compared to optical microscopes.

Numerical Aperture (NA): The resolution is directly proportional to the numerical aperture. Higher NA values result in better resolution. To enhance the numerical aperture, the microscope uses lenses with larger apertures and/or immersion techniques (using a higher refractive index medium between the lens and the specimen).

In summary, the resolution of a microscope is limited by the wavelength of the light used and the numerical aperture of the objective lens. Researchers and microscopists aim to improve the resolution to visualize and study finer details of specimens effectively. However, it's essential to keep in mind that even though the formula gives a theoretical limit, other factors like aberrations, diffraction, and the quality of the optics can also influence the practical resolution achieved in a microscope.