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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.
उत्तर
Focal length of the objective lens, f0 = 15 m = 15 × 102 cm
Focal length of the eyepiece, fe = 1.0 cm
a. The angular magnification of a telescope is given as:
`alpha = "f"_0/"f"_"e"`
= `(15 xx 10^2)/1.0`
= 1500
Hence, the angular magnification of the given refracting telescope is 1500.
b. Diameter of the moon, d = 3.48 × 106 m
Radius of the lunar orbit, r0 = 3.8 × 108 m
Let d' be the diameter of the image of the moon formed by the objective lens.
The angle subtended by the diameter of the moon is equal to the angle subtended by the image.
`"d"/"r"_0 = "d'"/"f"_0`
`(3.48 xx 10^6)/(3.8 xx 10^8 ) = "d'"/15`
∴ `"d'" = 3.48/3.8 xx 10^(-2) xx15`
= 13.74 × 10−2 m
= 13.74 cm
Hence, the diameter of the moon’s image formed by the objective lens is 13.74 cm.
संबंधित प्रश्न
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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?
A small telescope has an objective lens of focal length 140 cm and an eyepiece of focal length 5.0 cm. What is the magnifying power of the telescope for viewing distant objects when
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- the final image is formed at the least distance of distinct vision (25 cm)?
- 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?
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
State the condition under which a large magnification can be achieved in an astronomical telescope.
Write the two important factors considered to increase the magnifying power?
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Define magnifying power of a telescope. Write its expression.
The eyepiece of an astronomical telescope has a focal length of 10 cm. The telescope is focussed for normal vision of distant objects when the tube length is 1.0. m. Find the focal length of the objective and the magnifying power of the 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
Draw a labelled ray diagram showing the formation of an image by a refracting telescope when the final image lies at infinity.
With the help of a ray diagram explain the working of a reflecting telescope.
In an astronomical telescope in normal adjustment, a straight black line of length L is drawn on the objective lens. The eyepiece forms a real image of this line whose length is 𝑙. What is the angular magnification of the telescope?
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 | |||
