A converging lens and a diverging lens, separated by a distance of 20.0 cm, are

Question

A converging lens and a diverging lens, separated by a distance of 20.0 cm, are used in combination. The converging lens has a focal length of 14.0 cm. The diverging lens is of unknown focal length. An object is placed 19.0 cm in front of the converging lens; the final image is virtual and is formed 12.0 cm before the diverging lens. What is the focal length of the diverging lens? A converging lens and a diverging lens, separated by a distance of 20.0 cm, are used in combination. The converging lens has a focal length of 14.0 cm. The diverging lens is of unknown focal length. An object is placed 19.0 cm in front of the converging lens; the final image is virtual and is formed 12.0 cm before the diverging lens. What is the focal length of the diverging lens?

Explanation / Answer

:  Use the lensmaker's formula;

1/f = 1/o + 1/i

for the converging lens:

1/i = 1/f - 1/o = 1/0.14 - 1/0.19, .....=> i = 0.532 m

this is the position of the object for the diverging lens:

1/f = 1/0.532 + 1/0.8, .........=> f = 1/(1/0.53 + 1/0.8) = 1/3.136 = 0.31 m = 31cm

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