Draw a ray diagram to show the formation of real image of the same size as that of the object placed infront of a converging lens. Using this ray diagram establish the relation between $u, v$ and $f$ for this lens.

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Solution

Let distance of object AB from lens = u
Distance of image A'B' from lens = v
Focal length of lens = f.
Triangles ABC and A'B'C are similar
Similarly triangles PCF and A'B' are similar
But PC = AB
From sign convection, CB =-u, CB' = v CF = f and FB' =CB' - CF = v - f
or -u (v - f) = vf or - uv + uf = vf

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Draw a ray diagram to show the formation of real image of the same size as that of the object placed infront of a converging lens. Using this ray diagram establish the relation between u,v and f for this lens.

Let distance of object AB from lens = uDistance of image A'B' from lens = vFocal length of lens = f.Triangles ABC and A'B'C are similarSimilarly triangles PCF and A'B' are similarBut PC = ABFrom sign convection, CB =-u, CB' = v CF = f and FB' =CB' - CF = v - for -u (v - f) = vf or - uv + uf = vf

Draw a ray diagram to show the formation of real image of the same size as that of the object placed infront of a converging lens. Using this ray diagram establish the relation between $u, v$ and $f$ for this lens.