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Question

Derive lens formula 1v1u=1f .

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Solution

The figure above shows that the formation of a real, inverted and diminished image AB of the object AB placed beyond the centre of curvature at a distance u from the convex lens. Let v be the image distance,
According to Cartesian sign convention
Object distance (OB)=u
Image distance (OB)=+v
Focal length (OF1=OF2)=+f
From the geometry of the figure above, right angled ABO and ABO are similar.
ABAB=OBOB=v ........ (i)
Similarly, from the geometry of the figure above, right angled ODF2 and BAF2 are similar.
ODAB=OF2F2B2
ABAB=OF2F2B2 ( OD = AB, are the opposite sides of ABOD )
ABAB=OF2OBOF2
ABAB=fvf .......(ii)
From (i) and (ii),
uv=vvf
u(vf)=vf
uv+uf=vf
Dividing each term by uvf,
1f+1v=1u
1v1u=1f
This equation is called the 'Lens formula'.

660241_625831_ans_a21d7e1bb2384f31b976777942c0a768.png

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