Question

A giant refracting telescope at an observatory has an objective lens of focal length $15{\text{m}}$ . If an eyepiece of focal length $1 \cdot 0{\text{cm}}$ is used, then find the angular magnification of the telescope.
A) 1000
B) 1500
C) 2000
D) 3000

Answer 1

A telescope is an optical instrument that uses a multiple lenses system to observe an image of a distant object. The lens next to the eye of the observer is the eyepiece and the one next to the object is the objective. The telescope provides angular magnification of faraway objects and the angular magnification is the ratio of the focal length of the objective to the focal length of the eyepiece.

Formula used:
-The angular magnification of a telescope is given by, $m = \dfrac{{{f_o}}}{{{f_e}}}$ where ${f_o}$ is the focal length of the objective and ${f_e}$ is the focal length of the eyepiece.

Complete step by step solution:
Step 1: List the given focal lengths of the telescope.
The telescope consists of an objective and an eyepiece.

The focal length of the objective is given to be ${f_o} = 15{\text{m}}$ .

The focal length of the eyepiece is given to be ${f_e} = 1{\text{cm}}$ .

Step 2: Express the relation for the angular magnification of the telescope.

The angular magnification of the telescope can be expressed as $m = \dfrac{{{f_o}}}{{{f_e}}}$ -------- (1)

Substituting for ${f_o} = 15{\text{m}}$ and ${f_e} = 0 \cdot 01{\text{m}}$ in equation (1) we get, $m = \dfrac{{15}}{{0 \cdot 01}} = 1500$

$\therefore$ the angular magnification of the given telescope is obtained to be $m = 1500$.

Thus, the correct option is B.

Note: Light from the faraway object enters the objective and forms an image. This image is then magnified by the eyepiece and is seen by the observer. While substituting values of physical quantities in an equation make sure that all the quantities are expressed in their respective S.I units. If this is not the case, then the necessary conversion of units must be done. Here the focal length of the eyepiece was expressed in centimetres, ${f_e} = 1{\text{cm}}$. So we converted this into metres as ${f_e} = 0 \cdot 01{\text{m}}$before substituting in equation (1).