Question

Obtain an expression for magnification for simple microscope.

Answer 1

tana = AB/d---------(a)

In right angled triangle DOPE:

tanb = OP/PE-----

tanb = OP/p-------(b)-----

Since OP = AB = height of object

tanb = AB/p-------(c)-----

Putting the values of tana and tanb in equation (2)

M = (AB/p)/(AB/d)

M = d/p -----------------(d)

Using thin lens formula

Here P = + p, q = - d and f = + f

1/f = 1/-d + 1/p

1/f = -1/d + 1/p

Multiplying both sides by "d"

d/f = -d/d + d/p

d/f = -1 + d/p

1 + d/f = d/p

or  

d/p = 1 + d/f-----(e)

Comparing equation (e) and (d)

This expression indicates that for high magnification, focal length of magnifying glass should be small.