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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.
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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
A small telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6.0 cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?
- 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.
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 |
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
Write two important limitations of a refracting telescope over a reflecting-type 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.
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?
