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Draw a Labelled Ray Diagram of an Astronomical Telescope to Show the Image Formation of a Distant Object. - Physics

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ConceptOptical Instruments Telescope

Question

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.

Solution

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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Solution Draw a Labelled Ray Diagram of an Astronomical Telescope to Show the Image Formation of a Distant Object. Concept: Optical Instruments - Telescope.
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