Question

Derive m =I/O =V/U for a thin convex lens? Please tell me fast.

Answer 1

OF1=Focal length=f

OA=object distance=u

OA'=image distance=v

Triangle OAB similar to Triangle OA'B'

angleBAO=angle B'A'O=90°

so, angle AOB=angleA'B'O

A'B'/AB=OA'/OA ---------------(1)

Triangle OCF1 similar to Triangle F1A'B'

A'B'/OC=A'F1/OF1

OC=AB

A'B'/AB=A'F1/OF1=OF1-OA'/OF1

A'B'/AB=OF1-OA'/OF1---------------(2)

from eqn 1 and 2 we get

OA'/OA=OF1 - OA'/OF1

-v/-u= -f-(-v)/-f

v/u= f+v/f

-vf=-uf+uv

on dividing both sides by uvf we get

1/u=1/v+1/f

1/v-1/u=1/f

magnification m=height of image /height of object or m=v/u