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Question

Describe the compound microscope on the following headings
(i) Labelled Ray diagram of formation of image.
(ii) Magnifying power when final image is formed at least distance of distinct vision.

Solution
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Where,
O Objective lens, E Eye lens, AB Object, PQ Image
(ii) Calculation of magnification: Ratio of angle subtended by an image to the angle subtended by an object placed at least distance of distinct vision is called magnifying power of microscope.
If angle subtended by an image is β and angle by an object placed at D is given by α. Therefore, magnifying power.
m=βα .......... (i)
α=ABD
Where, D Least distance of distinct vision.
As eye is close to the eye lens, we can take the angle subtended at lens for human eye also.
Angle made by an image PQ
β=PQEQ=ABEB
or β=ABue
Where, ueEB Distance of image from eye lens.
Substituting above values in eqn. (i),
m=ABueABD=ABAB×Due ........... (ii)
Now, in similar triangle ΔAOB and ΔAOB,
ABAB=OBOB
From eqn. (ii), m=OBOB×Due
or m=vouo×Due
(By sign convention)
Where, uoOB Distance of object from objective lens, voOB Distance between objective to the image A'B'.
or m=VoDuoue ....... (iii)
When image is formed at least distance of distinct vision:
Form formula: 1f=1v1u
For eye lesn, 1fe=1ve1ue
or 1fe=1ve+1ue
But, Ve=D
1fe=1D1ue
or 1ue=1fe+1D
or Due=Dfe+1
Substituting this value in eqn. (iii), we get,
m=vouo(1+Dfe) ........ (iv)
Formula for magnification when image is formed at D magnification.
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