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Question

Describe the astronomical telescope on the basis of the following points:
(i) Labelled Ray diagram.
(ii) Derivation of formula for magnifying power, when final image is formed at the least distance of distinct vision.

Solution
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(i) Where, O Objective lens, O Eye lens, PQ Image.
(ii) Expression for magnifying power: If angle made by an object at least distance of distinct vision is α and angle made by an image is β. Then magnification.
m=βα .......... (i)
Object is situated at infinity, therefore angle subtended by an object on objective lens is said to be angle subtended by an object on eye.
Now, tanβ=PQOQ and tanα=PQOQ
As α and β are very small hence,
tanββ and tanαα
β=PQOQ and α=PQOQ
Putting the values of β and in eqn. (i), we get.
m=PQ/OQPQ/OQ=OQOQ ......... (ii)
By sign convention distance of P'Q' from Le=ue(ve)=OQ and focal length of objective lens Lo is
fo=OQ(+ve)
m=foue .......... (iii)
When image is formed at least distance of distinct vision.
From formula : 1f=1v1u
or 1fe=1ve1ue
or 1fe=1ve+1ue
But, ve=D
1fe=1D+1ue
or 1ue=1fe+1D
Substituting above value in eqn. (iii),
m=fo(1fe+1D)
m=fofe(1+feD)
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