Two converging lenses having focal lengths of f1 = 11.1 cm and f2 = 20.0 cm are

Question

Two converging lenses having focal lengths of f1 = 11.1 cm and f2 = 20.0 cm are placed = 50.0 cm apart, as shown in the figure below. The final image is to be located between the lenses, at the position x = 28.3 cm indicated.How far to the left of the first lens should the object be positioned?

Explanation / Answer

We have: AB---L1-----A'B'----L2---A1B1 ....d.........d'...d1........d'1 f1 = 10 cm ; f2 = 20cm d = 30cm l = d' + d1 = 40cm use: 1/f1 = 1/d + 1/d' with f1 = 10cm ; d = 30cm =>1/ d' = 1/10 - 1/30 = 1/15 =>d ' = 15 (cm because: d' + d1 = l = 40cm =>d1 = 40 - d' = 25 cm use 1/f2 = 1/d1 + 1/d'1 =>1/d'1 = 1/20 - 1/25 = 1/100 =>d'1 = 100 (cm) have:: | k1 | = A'B' / AB = d' / d = 15 / 30 = 1/2 =>A'B' = AB /2 (AB is the height of the object) =>A'B' = 3/2 = 1.5 cm _________ | k2 | = A1B1 / A'B' = d'1 / d1 = 100 / 25 = 4 =>A1B1 = 4A'B' = 4*1.5 = 6 (cm) Answer: 6 cm

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