Advertisements
Advertisements
प्रश्न
Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position. A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1.0 cm. If this telescope is used to view the Moon, find the diameter of the image of the Moon formed by the objective lens. The diameter of the Moon is `3.48 xx 10^6`m, and the radius of the lunar orbit is `3.48 xx 10^8`m.
Advertisements
उत्तर
When the final image is formed at the least distance of distinct vision
Magnifying power,
`M = beta/alpha`
α and β are small
∴ `M = tan β/tan α` ...(i)
In ΔA'B'C2 ,tan β = `("A"'"B"')/("C"_2"B"')`
In ΔA'B'C1, tanα = `("A"'"B"')/("C"_1"B"')`
From equation (i), we have:
`M = ("A"'"B"')/("C"_2"B"') xx ("C"_1"B"')/("A"'"B"')`
`"M"= ("C"_1"B"')/("C"_2"B"')`
Here,
`C_1B' = +f_0`
`C_2B' = -u_e`
`M = f_0/-u_e` ...(ii)
Using the lens equation `(1/ν - 1/u = 1/f)` for the eyepieces, we get
`1/(-D) - 1/(-u_c) = 1/f_e`
`-1/D + 1/u_c = 1/f_e`
`1/u_e = 1/f_e + 1/D`
`f_0/u_e = f_0/f_e (1 + f_e/D)`
`(-f_0)/u_e = (-f_0)/f_e (1 + f_e/D)`
M = `-f_0/f_e (1 + f_e/D)`
Angular magnification is:
`m_0 = |(f_0)/(f_e)| = |1500/1| = 1500`
Where, `"f"_0` is the focal length of the objective lens and fe is the focal length of the eye piece
Given, the diameter of the moon = `3.48 xx 10^6`m
The radius of the lunar orbit = `3.8 xx 10^8`m
The diameter of the image of the moon formed by the objective lens is given by d = af0
d = `"Diameter of the moon"/"Radius of the lunar orbit" xx f_0`
d = `(3.48 xx 10^6)/(3.8 xx 10^8) xx 15 = 13.74` cm
संबंधित प्रश्न
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
Write two important limitations of a refracting telescope over a reflecting-type telescope.
Define magnifying power of a telescope. Write its expression.
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
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.
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?
-
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 | |||
