An object is placed in front of a collecting lens with a focal length of 10 cm. At what distance should the object be placed

An object is placed in front of a collecting lens with a focal length of 10 cm. At what distance should the object be placed so that its actual image is 4 times larger than the object itself?

F = 10cm
we denote the distance from the object to the lens d = x, then its actual image
f = 4x
1 / F = 1 / d + 1 / f
1 / d = 1 / F-1 / f
1 / x = 1 / 10-1 / 4x
1 / x = 4x-10 / 40x
4×2-10x = 40x (* 4×2 – x squared)
4×2-50x = 0
4x (x-12.5) = 0
4x = 0 (not possible)
x-12.5 = 0
x = 12.5 cm (distance from object to lens)



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