Question

Draw a well labelled diagram to obtain the real image formed by an astronomical telescope in normal adjustment position. Define its magnifying power.
 You are given three lenses of power \[0.5\]D, \[4\]D and \[10\]D to design a telescope.
(i) Which lenses should be used as objective and eyepiece? Justify your answer.
(ii) Why is the aperture of the objective preferred to be large?

Answer 1

Hint: Astronomical telescope is an optical instrument which is used for observing distinct images of distant objects like stars, planets, etc. Magnifying power is directly proportional to the focal length of the objective lens and inversely proportional to the focal length of the eye piece. So we have to choose the correct option according to the given data.

Complete step-by-step solution:
The image formed by an astronomical telescope in normal adjustment position is given below.
Normal adjustment is the case in which the image is formed at infinity.
Magnifying power is defined as the ratio of angle subtended by the final image at eye to the angle subtended by the object seen directly ,when object and final image both lie at infinity.
Mathematically it can be given as -
Let us suppose the magnification is represented as m.
\[m=\dfrac{\tan \beta }{\tan \alpha }\]
\[\alpha \]and \[\beta \] are very small, therefore we can write
\[\beta \] =\[\tan \beta \]
\[\alpha \]=\[\tan \alpha \]
Suppose magnification equation becomes
\[m=\dfrac{\beta }{\alpha }\]
i) Power of the lens is inversely proportional to its focal length. A lens with less power will have larger focal length and the lens with more power will have small focal length.
The Object should be of large focal length and eyepiece should be of small focal length by which magnifying power will be increased and hence large magnification of the object will be observed.
So, the lens with power \[0.5\]D will be used as an objective and the lens with power \[10\]D will be used as an eyepiece in the telescope.
ii) An astronomical telescope should have an objective of large focal length and large aperture and an eyepiece of small focal length and small aperture. Large focal length is to get the magnifying image of an object and large aperture is to collect more light in the telescope .Also the light gathering power or the resolving power of the telescope is directly proportional to the diameter of the aperture, hence large aperture should be preferred. If the aperture is large then the image will be brighter and a clear image will be seen.

Note:Length of the telescope is the distance between objective lens and eye lens which will be the sum of focal length of eye lens and focal length of objective lens. Maximum magnifying power is obtained when the final image is at least distance. Minimum magnifying power is obtained when the final image is at infinity.