Advertisements
Advertisements
Question
- 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?
Advertisements
Solution
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.
RELATED QUESTIONS
Draw a labeled ray diagram to obtain the real image formed by an astronomical telescope in normal adjustment position. Define its magnifying power.
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.
Draw a ray diagram showing the image formation of a distant object by a refracting telescope ?
Write the two important factors considered to increase the magnifying power?
Write two important limitations of a refracting telescope over a reflecting-type telescope.
Define its magnifying power and write the expression for it?
A small telescope has an objective lens of focal length 150 cm and an eye piece of focal length 5 cm. If this telescope is used to view a 100 m high tower 3 km away, find the height of the final image when it is formed 25 cm away from the eye piece.
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 Galilean telescope is 27 cm long when focussed to form an image at infinity. If the objective has a focal length of 30 cm, what is the focal length of the eyepiece?
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?
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.
With the help of a ray diagram explain the working of a reflecting telescope.
Draw a labelled ray diagram showing the image formation by a refracting telescope. Define its magnifying power.
The magnifying power of an astronomical telescope in normal adjustment is 2.9 and the objective and the eyepiece are separated by a distance of 150 cm. Find the focal lengths of the two lenses.
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 | |||
