Q.3. Derive lens formula forconvex lens.

1.	Q.3. Derive lens formula forconvex lens.
Answer» Ans :- OF1=Focal length=fOA=object distance=uOA'=image distance=vTriangle OAB similar to Triangle OA'B'angleBAO=angle B'A'O=90°so, angle AOB=angleA'B'OA'B'/AB=OA'/OA ---------------(1) Triangle OCF1 similar to Triangle F1A'B' A'B'/OC=A'F1/OF1OC=ABA'B'/AB=A'F1/OF1=OF1-OA'/OF1A'B'/AB=OF1-OA'/OF1---------------(2) from eqn 1 and 2 we get OA'/OA=OF1 - OA'/OF1-v/-u= -f-(-v)/-fv/u= f+v/f-vf=-uf+uv on dividing both sides by uvf we get 1/u=1/v+1/f1/v-1/u=1/f magnification m=height of image /height of object or m=v/u

Answer»

Ans :- OF1=Focal length=fOA=object distance=uOA'=image distance=vTriangle OAB similar to Triangle OA'B'angleBAO=angle B'A'O=90°so, angle AOB=angleA'B'OA'B'/AB=OA'/OA ---------------(1)

Triangle OCF1 similar to Triangle F1A'B' A'B'/OC=A'F1/OF1OC=ABA'B'/AB=A'F1/OF1=OF1-OA'/OF1A'B'/AB=OF1-OA'/OF1---------------(2)

from eqn 1 and 2 we get OA'/OA=OF1 - OA'/OF1-v/-u= -f-(-v)/-fv/u= f+v/f-vf=-uf+uv

on dividing both sides by uvf we get 1/u=1/v+1/f1/v-1/u=1/f

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

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