Question

derivation of simple microscope

Answer 1



The apparent size of an object depends upon its visual angle subtended on the eye . ... Such a lens is called magnifying glass orsimple microscope .A magnifying glass forms an image at the least distance of distinct vision i.e 25cm from the eye and the object looks like a big sized object.

Answer 2

Mgnifying power of magnifying glass\M = b/a ---------(1) a and b are small angles, therefore we can take:a = tan a.
and.
b = tan b-------------------(2)Consider an object OP placed at a distance "p" within the focal length of a magnifying glass such that an erect ,virtual and magnified image IQ is produced at 25 cm from the eye.In right angled triangle DABE:tana = AB/EB-----ORtana = AB/d---------(a)In right angled triangle DOPE:tanb = OP/PE-----tanb = OP/p-------(b)-----Since OP = AB = height of objecttanb = 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 formulaHere P = + p, q = - d and f = + f1/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)
                                        M=1=d/f