 # Resolving Power of a Microscope and Telescope

Overview

Resolving power of a device is the capacity to see the objects that are located at a distance. Resolving power is the power of an optical device to distinguish between two firmly placed objects which are located at a distance, and produce their images.

Resolution is the minimum distance between two different objects in an image that can be distinguishable. It is also called a minimum resolvable distance. This term is not much used by the people who use a microscope and telescope. In scientific analysis, the resolution is described as the precision of an instrument to measure and record the variables of the sample under consideration.

Explanation

"Rayleigh criterion" is redirected here. Please do not confuse it with the Rayleigh roughness criterion.

The resolution of an imaging instrument is limited either by diffraction or by aberration. This causes blurring of the image. Aberration is a problem of geometrical optics and is solved by increasing the optical quality of the instrument. Whereas, diffraction arises due to the wave nature of light and is determined by the aperture of optical instruments. A Lens circular aperture is similar to that of a single slit experiment. When light passes through the lens, it interferes with itself, thereby creating a ring-shaped diffraction pattern called Airy pattern. This occurs when the front of the light is spherical or plane at the point of aperture exit.

According to Rayleigh's Formula:

θ = 1.220 $\frac{λ}{D}$

Where

θ = angular resolution (in radians),

λ = wavelength of light used, and

D = diameter of the lens' aperture.

Now, considering the diffraction through a circular aperture, we can state:

Resolving Power Definition

• Resolving power is opposite to the distance between two different objects, which can be resolved when viewed from an optical instrument.

• The optical instruments must be able to display two separate and individual images of the objects because they are two distinct, separate images.

• Suppose, if you see two stars by using a telescope, and the stars are very close to each other, these stars should not be displayed as one single star.

• The stars should be displayed as two separate stars. This ability of an optical device to display them as separate stars are called resolving power.

For Example: -

Let us consider two rooms, such that one room is lit and another room is dark. We can see things clearly in the lit room, whereas in the darkroom, we will not be able to see anything properly.

This is because the resolving power of our eyes is low in the darkroom, and hence we are not able to see properly.

More is the resolving power of a device, better will be the image quality and clarity, and things can be seen clearly.

## Difference Between Resolution and Magnification

 Resolution Magnification We can clearly see two different closely spaced objects located at a distance. It magnifies the size of objects. It distincts between two different objects. It is used to enlarge the objects.

Note:-

• Magnification and resolution are inversely proportional to each other. So, when magnification increases, the resolution decreases, and vice versa.

• Resolution is the distinctness of two different objects located closely.

• Magnification is the enlargement of the size of an object.

• The resolving power or resolution of an objective lens is measured by its capacity to distinguish between two different lines or points in an image. The more the resolving power, the less will be the distance between two lines or points. The larger the N.A, the more will be its resolving power.

Resolving Power Formula

The resolving power formula is used for determining a resolution.

Resolving Power of Telescope:

Telescopes subtend a very small angle for viewing objects like binary stars, individual stars, distant galaxies, quasars, and planets, making it very easy to study and view them. Large apertures are needed to resolve the power of a telescope. We can use Rayleigh's formula to evaluate the resolving power of the telescope formula.

Based on the Rayleigh's formula the angular separation between two distant objects should be

Resolving Power = D/d = a/1.22λ

Where,

a = width of the rectangular slit

D = distance of objects of the telescope.

If the diameter d is greater, the resolution will be better. The astronomical optical telescopes usually have a mirror of large diameters, such as 10m, to get the desired resolution. Large wavelengths help in reducing the resolving power of the telescope, and that's why the radio and microwave telescopes require larger mirrors.

Resolving Power of Microscope:

When it comes to microscopes, the resolving power is inversely proportional to the distance between the two objects. A microscope can be resolved, and this is done by using Abbe's criterion, which was given by Ernst Abbe in the year 1873.

It states that:

The resolution R depends on the angular aperture (here the resolution is measured in terms of distance, and is not the angular resolution which is considered in the previous part).

The resolving power of microscope formula is given by:

R = $\frac{1.22λ}{NA_{condenser}+NA_{Objective}}$  Where NA = n sinθ

Where,

NA = the numerical aperture,

θ = half of the angle α of the lens, which depends on the focal length and the diameter of the lens,

n = refractive index of the medium between the specimen and the lens, and

λ = wavelength of light that is emerging from the object under consideration.

The diffraction of the aperture restricts the resolving power of the light microscope. An optical system cannot be able to form a perfect image of a point due to diffraction. For a resolution to occur, the first-order diffracted beam & direct beam must be collected as an objective of the microscope.