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प्रश्न
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.
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उत्तर
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.
संबंधित प्रश्न
- A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece of focal length 1.0 cm is used, what is the angular magnification of the telescope?
- If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is 3.48 × 106 m, and the radius of lunar orbit is 3.8 × 108 m.
Why should the objective of a telescope have large focal length and large aperture? Justify your answer.
Draw a ray diagram depicting the formation of the image by an astronomical telescope in normal adjustment.
Draw a labelled ray diagram of an image formed by a refracting telescope with the final image formed at infinity. Derive an expression for its magnifying power with the final image at infinity
Describe briefly the two main limitations and explain how far these can be minimized in a reflecting telescope ?
"A telescope resolves whereas a microscope magnifies." Justify this statement ?
(i) What is meant by resolving power of a telescope?
(ii) State any one method of increasing the resolving power of an astronomical telescope.
An astronomical telescope uses two lenses of powers 10 dioptres and 1 dioptre. If the final image of a distant object is formed at infinity, calculate the length of the telescope
A small telescope has an objective lens of focal length 140 cm and an eyepiece of focal length 5.0 cm. Find the magnifying power of the telescope for viewing distant objects when
- the telescope is in normal adjustment,
- the final image is formed at the least distance of distinct vision.
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 | |||
