Question

A small telescope has an objective lens of focal length $140 \mathrm{~cm}$ and an eyepiece of focal length $5.0 \mathrm{~cm}$. What is the magnifying power of the telescope for viewing distant objects when
(a)the telescope is in normal adjustment (i.e., when the final image is at infinity)?
(b) the final image is formed at the least distance of distinct vision $(25 \mathrm{~cm}) ?$

Answer 1

A telescope is a type of focal converter, which implies that it is used to view objects at infinity, and the telescope's image appears at infinity. At infinity, the short focal length lens forms an image of the long focal length lens image. Calculate Focal length of the object and eye piece and the least distance of the distance vision. Calculate magnification by taking the ratio of the focal length.

Complete step by step solution:
The primary mirror is located in a reflector at the lower end of the telescope tube and has an extremely thin metal film, such as aluminums, coating its front surface. The back of the mirror is usually made of glass, although it has been used from time to time with other materials.
Focal length of the objective lens, $f_{o}=140 \mathrm{~cm}$
Focal length of the eyepiece, $f_{\mathrm{e}}=5 \mathrm{~cm}$
Least distance of distinct vision, $d=25 \mathrm{~cm}$
(a) When the telescope is in normal adjustment, its magnifying power is given as:
$m=\dfrac{f_{o}}{f_{e}}$
$\therefore m=\dfrac{140}{5}=28$
The magnifying power of the telescope for viewing distant objects when the telescope is in normal adjustment is $m=28$
(b) When the final image is formed at $d$,the magnifying power of the telescope is given as:
$\dfrac{f_{o}}{f_{e}}\left[1+\dfrac{f_{e}}{d}\right]$
$=\dfrac{140}{5}\left[1+\dfrac{5}{25}\right]$
$=28[1+0.2]$
$=28 \times 1.2=33.6$
$\therefore m=33.6$
The magnifying power of the telescope for viewing distant objects when the final image is formed at the least distance of distinct vision is $m=33.6$

Note:
In an optical system, an objective is the lens closest to the object that forms the initial image. In a telescope, an intermediate image is the image formed by the objective lens. There are two lenses in a simple telescope, called a refractor. The big one collects and amplifies the light from a distant object, so that the image is much brighter than what the eye normally sees.At the centre of the objective, a second lens is placed and provides the magnification you need to study the objects.