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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
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 |
State the condition under which a large magnification can be achieved in an astronomical telescope.
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Write two important limitations of a refracting telescope over a reflecting-type telescope.
Define magnifying power of a telescope. Write its expression.
Draw a labeled ray diagram of a reflecting telescope. Mention its two advantages over the refracting telescope.
Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position. A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1.0 cm. If this telescope is used to view the Moon, find the diameter of the image of the Moon formed by the objective lens. The diameter of the Moon is `3.48 xx 10^6`m, and the radius of the lunar orbit is `3.48 xx 10^8`m.
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?
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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 | |||
A small telescope has an objective of focal length 140 cm and an eye piece of focal length 5.0 cm. The magnifying power of telescope for viewing a distant object?
