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प्रश्न
- 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?
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उत्तर
Focal length of the objective lens, fo = 140 cm
Focal length of the eyepiece, fe = 5 cm
(a) In normal adjustment, the separation between the objective lens and the eyepiece = fo + fe = 140 + 5 = 145 cm
(b) Height of the tower, h1 = 100 m
Distance of the tower (object) from the telescope, u = 3 km = 3000 m
The angle subtended by the tower at the telescope is given as:
θ = `"h"_1/"u"`
= `100/3000`
= `1/30` rad
The angle subtended by the image produced by the objective lens is given as:
θ = `"h"_2/"f"_"o" = "h"_2/140 "rad"`
Where,
h2 = Height of the image of the tower formed by the objective lens
`1/30 = "h"_2/140`
`"h"_2 = 140/30`
∴ h2 = 4.7 cm
Therefore, the objective lens forms a 4.7 cm tall image of the tower.
(c) Image is formed at a distance, d = 25 cm
The magnification of the eyepiece is given by the relation:
`"m" = 1 + "d"/"f"_"e"`
= `1 + 25/5`
= 1 + 5
= 6
Height of the final image = mh2 = 6 × 4.7 = 28.2 cm
Hence, the height of the final image of the tower is 28.2 cm.
संबंधित प्रश्न
Draw a schematic ray diagram of a reflecting telescope showing how rays coming from a distant object are received at the eyepiece.
Draw a ray diagram depicting the formation of the image by an astronomical telescope in normal adjustment.
You are given three lenses of power 0.5 D, 4 D, and 10 D to design a telescope.
1) Which lenses should be used as objective and eyepiece? Justify your answer.
2) Why is the aperture of the objective preferred to be large?
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
With regard to an astronomical telescope of refracting type~ state how you will increase its:
1) magnifying power
2) resolving power
State the condition under which a large magnification can be achieved in an astronomical telescope.
Describe briefly the two main limitations and explain how far these can be minimized in a reflecting telescope ?
Write two important limitations of a refracting telescope over a reflecting-type telescope.
Define its magnifying power and write the expression for it?
Draw a labeled ray diagram of a reflecting telescope. Mention its two advantages over the refracting telescope.
A giant refracting telescope at an observatory has an objective lens of focal length 15 m. If an eyepiece lens of focal length 1.0 cm is used, find 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 3.42 × 106 m and the radius of the lunar orbit is 3.8 × 108 m.
A lady cannot see objects closer than 40 cm from the left eye and closer than 100 cm from the right eye. While on a mountaineering trip, she is lost from her team. She tries to make an astronomical telescope from her reading glasses to look for her teammates. (a) Which glass should she use as the eyepiece? (b) What magnification can she get with relaxed eye?
(i) What is meant by resolving power of a telescope?
(ii) State any one method of increasing the resolving power of an astronomical telescope.
Draw a labelled ray diagram showing the formation of an image by a refracting telescope when the final image lies at infinity.
Define the term ‘resolving power of a telescope’.
Draw a ray diagram of Astronomical Telescope for the final image formed at infinity
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. |
- Why the image formed at infinity is often considered most suitable for viewing. Explain
- In modern microscopes, multicomponent lenses are used for both the objective and the eyepiece. Why?
- 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.
With the help of a ray diagram explain the working of a reflecting telescope.
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?
