Question

Write the formula for the limit of resolution of the telescope and explain the symbols used.

Answer 1

Hint: In this question we have been asked to write the formula for limit of resolution of a telescope. Therefore, to answer this question, we shall first define what is the limit of resolution. We shall also state the factors this limit mostly depends on. The limit of resolution is the distance between two points in the object that are just resolved in the image.

Complete answer:
The resolution limit or resolving power of any optical instrument is its ability to separate the images of two objects which are very close to each other. According to Rayleigh’s criterion, the two images are just resolved if the central maximum of one image falls on the first minimum of the diffraction pattern of the second image. The telescope has a very large aperture. Therefore, it has greater resolving power.
The minimum angular separation of two sources that can be distinguished by telescope depends on wavelength of light and on the diameter of the telescope. The angle between the separation is known as limit of resolution or diffraction limit. The resolution limit is a dimensionless quantity.
The formula for limit of resolution is given by,
$$\theta ={\displaystyle \frac{1.22\lambda }{D}}$$
Where,
$$\theta$$ is the limit of resolution
$$\lambda$$ is the wavelength of the light
D is the diameter of the telescope

Note:
In general, when the diameter of the telescope is increased the resolution limit of the telescope increases. As the units of wavelength and diameter is the same, the limit of resolution has no unit. The resolving power of the human eye is 20/20. Resolving power is sometimes mistaken as magnification of image. However, magnification is the enlargement of image. Resolution limit is the ability of an optical instrument to show two closely placed objects as discrete.