Two converging lenses having focal lengths of f 1 = 11 cm and f 2 = 18 cm are pl

Question

Two converging lenses having focal lengths of f1 = 11 cm and f2 = 18 cm are placed 47 cm apart as shown in Figure. The final inverted image is to be located between the lenses at the position 37 cm to the right of the first lens. How far to the left of the first lens should the object be positioned? Express the answer (in cm) with one decimal place.

Two converging lenses having focal lengths of f1 = 11 cm and f2 = 18 cm are placed 47 cm apart as shown in Figure. The final inverted image is to be located between the lenses at the position 37 cm to the right of the first lens. How far to the left of the first lens should the object be positioned? Express the answer (in cm) with one decimal place.

Explanation / Answer

f1 = 11 cm
f2 = 18 cm

distance between two lenses, d = 47 cm

image distance for the second lense, v2 = -10 cm

we know,

1/u2 + 1/v2 = 1/f2

1/u2 = 1/f2 - 1/v2

1/u2 = 1/18 + 1/10

==> u2 = 6.43 cm (oject distance for the second lense)


v1 = d - u2 = 47 - 6.43 = 40.57 cm (image distance fro the first lense)

1/u1 + 1/v1 = 1/f1

1/u1 = 1/f1 - 1/v1

1/u1 = 1/11 - 1/40.57

==>u1 = 15.1 cm (oject distance for the first lense)

so, the object should be placed at 15.1 cm from the first lense

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