Telescopes, working, magnification, Practice problems, FAQs

Q: Why is the size of the objective bigger in a telescope?

Answer: Objective has a larger aperture than that of the eyepiece in case of a telescope so that sufficient light is incident on the telescope from distant objects and a clear image is formed.

Have you slept on your terrace at night? You will see the beautiful and shining stars and moon. But does it look so actually? When you see the moon from near, it has various mountains and valleys and looks very rough. But how we will see them so closely. In physics we have a device telescope that helps in viewing objects which are distant. Lets understand more about

telescopes and their working!

Table of content

What is a telescope?
Working of telescope
Magnification of a telescope
Practice problems
FAQs

What is a telescope?

A telescope is an optical instrument which is used to get a magnified image of a distant object. Like a microscope it also has an objective and an eyepiece. But here, the objective has a large focal length and a much larger aperture than the eyepiece.The below figure shows a modern telescope.

Working of telescope

A telescope is used to view an object that is at a very distant place. Hence a telescope needs at least two lenses of different sizes. The first lens(bigger one) forms a diminished image which is nearer to its focal point. Every telescope is designed in such a way so that the real and inverted image formed by the first lens is within or at the focal distance of the second lens. Now with the help of a second magnifying lens (smaller one), we get an enlarged image that is virtual. The final image formed by the second lens will be inverted with respect to the object.

Now let's find the magnification of a telescope.

Magnification of a telescope

For a telescope the magnifying power M is the ratio of the angle subtended at the eye by the final image to the angle which the object subtends at the lens (referring above figure). Hence

As the object is at infinity, the angles will be very small.

Now angular size of object

And angular size of image

Then magnification

Now consider two cases:

Case-1 When the image is formed at near point (v_e=-D)

Applying lens formula for eyepiece

Substituting the value of in the formula of magnifying power, we get,

This is magnification when the final image is formed at a near point.

Here the length of telescope tube is

Case-2 When the image is formed at infinity

Again applying lens formula for eyepiece

On substituting the value of in the formula of magnifying power, we get,

This is magnification when the image is formed at infinity.

In this case the length of telescope tube is

From both the cases we can conclude that when an image is formed at a near point the magnification is greater than the image formed at infinity. At infinity magnification is minimum.

Practice problem

Q1. An astronomical telescope has an objective of focal length 40 cm and an eyepiece of focal length 4 cm. To view an object which is at 200 cm away from the objective, the length of telescope must be:

A. 54.0 cm
B. 37.3 cm
C. 46.0 cm
D. 50.0 cm

Answer: Given f_o=40 cm

f_e=4 cm

u_o=-200 cm

Using lens formula for objective lens

so length of telescope

L=v_o+f_e

L=50+4

L=54 cm

Hence, Option (A) is correct.

Q2. A simple telescope has two convex lenses, the objective and the eyepiece, which have a common focal point. The focal length of the objective is 1.0 meter. If the angular magnification of the telescope is 10, find the optical path length between objective and eyepiece?

A. 0.1 m
B. 0.9 m
C. 1.0 m
D. 1.1 m

Answer: Given f_o=1.0 m

M=10

Magnification of the telescope:

f_e=0.1 m

The optical path length between objective and eyepiece means length of tube and is given by

L=1+0.1

L=1.1 m

Hence, Option (D) is correct.

Q3. Consider an astronomical telescope with an eyepiece of a focal-length of 5 cm. If the angular magnification in normal adjustment is 10, find angular magnification when the final image is at least distance of distinct vision (25 cm) from the eyepiece.

A. 10
B. 12
C. 50
D. 60

Answer: Given f_e=5 cm

When image is formed at infinity magnification

As we know

f_o=50 cm

When image is formed at near point

Magnification

M₂₅=12

Hence, Option (B) is correct.

Q4. An astronomical telescope of angular magnification 10 has a length of 44 cm. What is the focal length of the objective?

A. 44 cm
B. 440 cm
C. 40 cm
D. 4 cm

Answer: Given

L=44 cm

As we know

Magnification

And length of telescope

Solving equations (i) and (ii)

44=10f_e+f_e

44=11f_e

f_e=4

Hence, Option (C) is correct.

FAQs

Question 1. Why is the size of the objective bigger in a telescope?
Answer: Objective has a larger aperture than that of the eyepiece in case of a telescope so that sufficient light is incident on the telescope from distant objects and a clear image is formed.

Question 2. What is an astronomical telescope?
Answer: Telescopes used for viewing distant stars and planets are called Astronomical telescopes.

Question 3. What is a terrestrial telescope?
Answer: A telescope which is used to view distant objects on earth is called a terrestrial telescope.

Question 4. What size of telescope is enough to see the ring of Saturn?
Answer: The ring of Saturn is visible in a telescope with 25X.