Two thin lenses with a focal length of magnitude 17.0 cm, the first diverging and the second converging, are located 12.8 cm apart. An object 3.40 mm tall is placed 28.3 cm to the left of the first (diverging) lens. How far from this first lens is the final image formed?

1.93 cm

Explanation:

The Image Equation for the first lens will be

1/f1 = 1/do - 1/d1

Where f1 = 17cm and d1 = 28.3cm

1/do = 1/f1 + 1/d1

= 1/17 + 1/ 28.3

do = 10.62cm

This image (which is real, inverted, and enlarged) becomes the object for the second lens as we again apply the Image Equation for the second lens

1/ f2 = 1/d2 + 1/d

Since the lenses are 12.8 cm apart, the image formed 10.62 cm to the left of lens #1 is located 2.18 cm to the right of lens #2 so the object distance, then, is

1/d2 = 1/f + 1/d

= 1/17 + 1/2.18

d2 = 1.93cm

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