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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
With regard to an astronomical telescope of refracting type~ state how you will increase its:
1) magnifying power
2) resolving power
Describe briefly the two main limitations and explain how far these can be minimized in a reflecting telescope ?
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Write two important limitations of a refracting telescope over a reflecting-type telescope.
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.
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.
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?
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?
