Explain the Numerical Aperture?

Numerical aperture is a characteristic of each lens and is printed on the lens. It can be defined as a function of the diameter of the objective lens in relation to its focal length. It depends on the refractive index (η) of the medium in which the lens works and also upon the objective itself. Theta (φ) is defined as half of the angle of the cone of light entering an objective. Sin φ cannot be more than 1. Therefore, the lens working in air with refractive index 1 can have N.A.1. η will have to be increased for increasing the resolution. This can be done by using the mineral oil. Wavelength is also an important factor in resolution. With shorter wavelength, the resolving power increases. Just like magnification, resolution also has a limit. By decreasing wavelength, resolving power of the lens cannot be increased indefinitely because -

(a) the visible portion of the electromagnetic spectrum is very narrow and borders of very short wavelengths are found in ultraviolet range of spectrum.

(b) This relationship of Resolving Power with λ is valid only when light rays are parallel. As such 'Resolving Power' is also dependent on another factor, i.e., refractive index. When the light passes from air to glass slide, and from glass slide to air, there is a loss of light due to bending of rays. This reduces the numerical aperture and thus the resolving power of the lens. This loss in light can be compensated by using mineral oil in between glass slide and objective lens. Mineral oil is a colourless liquid having same refractive index as glass. This does decrease the bending of ray so that more light rays enter the objective lens thus increasing the resolving power. Proper specimen illumination is also important in determining resolution.