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.

Answer 1

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 f_e are in denominator.

This formula contains f_oand f_e in denominator. Therefore, both the objective and the eyepiece of a compound microscope must have short focal lengths.