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)|`

*f*_{0} and *f*_{e} are in denominator.

This formula contains *f*_{o}and *f*_{e} in denominator. Therefore, both the objective and the eyepiece of a compound microscope must have short focal lengths.

Concept: Optical Instruments - The Microscope

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