A converging lens with a focal length of +20.0 cm is located 8.10 cm to the left

Question

A converging lens with a focal length of +20.0 cm is located 8.10 cm to the left of a diverging lens having afocal length of -14.5 cm. If an objectis located 35.4 cm to the left of theconverging lens, locate and describe completely the final imageformed by the diverging lens.

1 __cm (image location with respect to the second lens)
2__ (magnification of image)

Explanation / Answer

For converging lens the image is located at        1 /i1 = 1 / f1 - i /p1 ==>     = 1 / 20 - 1 / 35.4 ==> i1 = 46 cm Slope m = -i1 / p1 = - 46 / 35.4 = - 1.29, the image isinverted This image is object to lens 2 with p2 = -(35.4 - 8.10)= - 27.3 cm            1 / i2 = 1 / f2 - 1 / p2                     = 1 / -14.5 - 1 / -27.3      ==> i2 = -31 cm it isvirtual magnification m = (-i1/p1) x (-i2/p2) = (-46 / 35.4) x-(-31/-27.3)                                                          = + 1.4 so image has the size orientation as the object.

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