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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.
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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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An astronomical telescope is to be designed to have a magnifying power of 50 in normal adjustment. If the length of the tube is 102 cm, find the powers of the objective and the eyepiece.
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.
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(i) What is meant by resolving power of a telescope?
(ii) State any one method of increasing the resolving power of an astronomical telescope.
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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.
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?
