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Question
Draw a labelled ray diagram of an astronomical telescope to show the image formation of a distant object. Write the main considerations required in selecting the objective and eyepiece lenses in order to have large magnifying power and high resolution of the telescope.
Solution
Astronomical telescope
When the final image is formed at the least distance of distinct vision:
Magnifying power, `M =β/α`
Since α and β are small, we have:
∴ `M= tanβ/tanα ...... (1)`
In `ΔA'B'C_2, tanβ = (A'B')/(C_2B') `
In `ΔA'B'C_1, tanβ = (A'B')/(C_2B') `
From equation (i), we get:
`M = (A'B')/(C_2B') xx (C_1B')/(A'B')`
\[\Rightarrow\] `M = (C_1B')/(C_2B')`
Here, `C_1B' = +f_0`
\[\Rightarrow\] `C_2B' = -u_e`
\[\Rightarrow\] `M = f_0/ -u_e .......... (2)`
Using the lens equation `(1/v-1/u=1/f)`for the eyepieces `(1/-D-1/-u_e=1/f_e,)`we get:
`(-1/D+1/u_e=1/f_e)`
\[\Rightarrow\] `(1/u_e=1/(f_e)+1/D)`
\[\Rightarrow\] `(f_0)/u_e =(f_0)/(f_e )(1+f_e/D)`
\[\Rightarrow\] `(-f_0)/u_e =(-f_0)/(f_e )(1+f_e/D) or M = -f_0/(f_e) (1+f_e/D) `
In order to have a large magnifying power and high resolution of the telescope, its objective lens should have a large focal length and the eyepiece lens should have a short focal length.
RELATED QUESTIONS
Draw a schematic ray diagram of a reflecting telescope showing how rays coming from a distant object are received at the eyepiece.
A small telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6.0 cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?
- For the telescope is in normal adjustment (i.e., when the final image is at infinity)? what is the separation between the objective lens and the eyepiece?
- If this telescope is used to view a 100 m tall tower 3 km away, what is the height of the image of the tower formed by the objective lens?
- What is the height of the final image of the tower if it is formed at 25 cm?
You are given the following three lenses. Which two lenses will you use as an eyepiece and as an objective to construct an astronomical telescope ? Give reason
| Lenses | Power (D) | Aperture (cm) |
| L1 | 3 | 8 |
| L2 | 6 | 1 |
| L3 | 10 | 1 |
Draw a ray diagram showing the image formation of a distant object by a refracting telescope ?
Define its magnifying power and write the expression for it?
Read the following paragraph and answer the questions.
| A number of optical devices and instruments have been designed and developed such as periscope, binoculars, microscopes and telescopes utilising the reflecting and refracting properties of mirrors, lenses and prisms. Most of them are in common use. Our knowledge about the formation of images by the mirrors and lenses is the basic requirement for understanding the working of these devices. |
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- Write two points of difference between a compound microscope and an astronomical telescope
OR
Write two distinct advantages of a reflecting type telescope over a refracting type telescope.
Draw a labelled ray diagram showing the image formation by a refracting telescope. Define its magnifying power.
Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power.
Read the passage given below and answer the question that follows.
| There are two types of optical instruments: Microscopes and Telescopes. Microscopes are used to magnify very tiny objects whereas telescopes are used to study distant objects. Both of them deploy convex lenses. In his telescope, Newton used a large parabolic mirror to collect light from the stars and reduce aberrations. |
- Rohit observed the launch of Chandrayan 3 with the help of an optical instrument. Name the instrument used by him.
- State any one advantage of a reflecting telescope over a refracting telescope.
- Which instrument is used to study the structure of a virus?
- What is the ability of an optical instrument to form enlarged images called?
-
What is the difference between a compound microscope and an astronomical telescope (refracting type), as far as their lenses are concerned?
Useful Constants & Relations:
| 1 | Charge of a proton | e | 1.6 × 10-19 C |
| 2 | Speed of light in vacuum | c | 3 × 108 ms-1 |
| 1 u = 931 MeV | |||
