Question

Draw a ray diagram showing the image formation by a compound microscope. Hence obtained expression for total magnification when the image is formed at infinity.

Answer 1

A compound microscope consists of two convex lenses co-axially separated by some distance. The lens nearer to the object is called the objective. The lens through which the final image is viewed is called the eyepiece.

Magnifying power, when final image is at infinity:

The magnification produced by the compound microscope is the product of the magnifications produced by the eyepiece and objective.

`∴M = M_e xx M_0            ...... (1)`

Where, M_e and M₀ are the magnifying powers of the eyepiece and objective respectively.

If u₀ is the distance of the object from the objective and v₀ is the distance of the image from the objective, then the magnifying power of the 

objective is `M_0 = (h')/h =L/f_0  ( using tanβ = (h/f_0) = =(h/L))`

Where, h, h' are object and image heights respectively and f₀ is the focal length of the objective.

L is the tube length i.e. the distance between the second focal point of the objective and the first focal point of the eyepiece.

When the final image is at infinity, `M_e = D/f_e`

Magnifying power of compound microscope,`M = M_0 xx M_e = L/f_0  xx D/f_e`