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Question
Draw the labelled ray diagram for the formation of image by a compound microscope.
Derive the expression for the total magnification of a compound microscope. Explain why both the objective and the eyepiece of a compound microscope must have short focal lengths.
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Solution
Show L in figure
`tan beta = h/(f_0) .... (1)`
`tan beta = h'/L ..... (2)`
`h'/h =Lf_0` [Using (1) and (2)]
`m_0 = h'/h = L/f_0` [Magnification due to objective]
`m_e = 1+D/f_e`
Net magnification (m) =`m_0m_e`
`|m = (L/f_0) (D/f_e)|`
f0 and fe are in denominator.
This formula contains foand fe in denominator. Therefore, both the objective and the eyepiece of a compound microscope must have short focal lengths.
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