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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
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 |
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.
How is the working of a telescope different from that of a microscope?
The focal lengths of the objective and eyepiece of a microscope are 1.25 cm and 5 cm respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 in normal adjustment.
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.
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.
(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
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.
Draw a ray diagram for the formation of image of an object by an astronomical telescope, in normal adjustment. Obtain the expression for its magnifying power.
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 | |||
A telescope in which the eye lens used is concave, so that the final image is erect, is popularly called a:
Which type of telescope uses a convex lens as the eyepiece, since there is no necessity for an erect image?
In the working idea of a telescope's magnifying power, the beam of incident rays is inclined at an angle \[\alpha\] with the principal axis, while the emergent beam is inclined at a greater angle \[\beta\]. This produces:
Which type of telescope uses two convex lenses, with a large objective and a small eyepiece?
Modern telescopes often use a concave mirror rather than a lens for the objective primarily because:
