Question

Draw a labelled ray diagram showing the formation of image by a compound microscope when final image is formed at least distance of distinct vision. Derive an expression for its magnifying power for this case.

Answer 1

Magnifying power (M) = m_o × m_e

Magnification by object (mo) = `"image height'/"object height"`

= `v_o/u_o`

Since the object is near the focal point:

m_o ≈ `L/f_o`

 Where L = tube length.

The eyepiece acts as a simple microscope:

m_e = `1 + D/f_e`

Total magnifying power (M) = `L/f_o  (1 + D/f_e)`

Where:

L = Tube length

f_o = Focal length of objective

f_e = Focal length of eyepiece

D = Least distance of distinct vision