Name: Angular Magnification and Magnifying Power
Uploaded: 2019-07-19
Duration: 7 min 43 s
Description: Angular magnification can be used to assess the size of the object as it appears to the eye. To learn more about angular magnification produced by an optical...

Question

Draw a ray-diagram of an astronomical telescope and derive an expression for its magnifying power when the image is formed at the least distance of distinct vision.

Accepted Answer

An astronomical telescope is an optical instrument used to see heavenly objects like stars, planets, etc. The image of such a distant object formed by the telescope subtends a large visual angle at the eye, so that the object appears quite large to the eye.

It consists of a long cylindrical metallic tube carrying at one end an achromatic convex lens of large focal length and large aperture which is called the ‘objective lens’. At the other end of the tube is fitted a smaller tube which can be moved in and out in the bigger tube by a rack and pinion arrangement. At the other end of the smaller tube is fitted an achromatic convex lens of small focal length and small aperture which is called the ‘eye-piece’. Cross-wires are mounted in the smaller tube at the focus of the eye-piece.

The magnifying power of astronomical telescope is given by,

$M = \frac{β}{\propto} . . . . . . (i)$

Since angles are very small,

$M = \frac{\tan β}{\tan \propto} = \frac{\frac{A' B'}{EA'}}{\frac{A' B'}{OA'}}$ or

$M = \frac{OA'}{EA'}$ or

$M = - \frac{f_{0}}{u_{e}}$

This is the general formula for magnifying power.

When the final image is formed at least distance of distinct vision,

$M = - \frac{f_{o}}{f_{e}} (1 + \frac{f_{e}}{D})$ .

Draw a ray-diagram of an astronomical telescope and derive an expression for its magnifying power when the image is formed at the least distance of distinct vision.

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