The distance between object and the screen is D. Real images of an object are formed on the screen for two positions of a lens separated by a distance d. The ratio between the sizes of two images will be:

Monjur Alahi

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Salim Ahmed Kawsar

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d(object and screen) = D = u + v 

and d = v – u 

Thus, d + D = 2v 

∴ v = [(d + D) / 2] and u = [(D – d) / 2] 

∴ m1 = (I1 / O) = (v/u) = [{D + (d/2)} / {D – (d/2)}] = [(D + d) / (D – d)] 

m2 = (I2 / O) = (u/v) = [{D – (d/2)} / {D + (d/2)}] = [(D – d) / (D + d)] 

∴ (I1 / I2) = [(D + d)2 / (D – d)2]

Hence, (I2 / I1) = [(D – d)2 / (D + d)2].

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