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प्रश्न
Draw a labelled ray diagram of an astronomical telescope to show the image formation of a distant object. Write the main considerations required in selecting the objective and eyepiece lenses in order to have large magnifying power and high resolution of the telescope.
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उत्तर
Astronomical telescope
When the final image is formed at the least distance of distinct vision:
Magnifying power, `M =β/α`
Since α and β are small, we have:
∴ `M= tanβ/tanα ...... (1)`
In `ΔA'B'C_2, tanβ = (A'B')/(C_2B') `
In `ΔA'B'C_1, tanβ = (A'B')/(C_2B') `
From equation (i), we get:
`M = (A'B')/(C_2B') xx (C_1B')/(A'B')`
\[\Rightarrow\] `M = (C_1B')/(C_2B')`
Here, `C_1B' = +f_0`
\[\Rightarrow\] `C_2B' = -u_e`
\[\Rightarrow\] `M = f_0/ -u_e .......... (2)`
Using the lens equation `(1/v-1/u=1/f)`for the eyepieces `(1/-D-1/-u_e=1/f_e,)`we get:
`(-1/D+1/u_e=1/f_e)`
\[\Rightarrow\] `(1/u_e=1/(f_e)+1/D)`
\[\Rightarrow\] `(f_0)/u_e =(f_0)/(f_e )(1+f_e/D)`
\[\Rightarrow\] `(-f_0)/u_e =(-f_0)/(f_e )(1+f_e/D) or M = -f_0/(f_e) (1+f_e/D) `
In order to have a large magnifying power and high resolution of the telescope, its objective lens should have a large focal length and the eyepiece lens should have a short focal length.
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| 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
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OR
Write two distinct advantages of a reflecting type telescope over a refracting type telescope.
With the help of a ray diagram explain the working of a reflecting telescope.
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Reason: Magnifying power of an astronomical telescope varies directly with focal length of the objective lens.
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?
