Question

The optical axis runs from left to right. At position 0.0 there is a converging lens with f=2.0 cm. 5 cm to the right of the lens is a diverging mirror with f=-1.5 cm. Parallel rays from the far left are focused to a point at two locations on the optical axis. Find the position of each location, giving your answer as a distance left or right of the lens.

Answer 1

I have one doubt from the question, why is the focal length of diverging mirror is given as negative ??? The focal length is diverging mirror is usually positive , not negative

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Anyway,

The question is basically asking for image distances formed by converging lens and diverging mirror.

The object is at the "far left" means it is at infinity, so image due to converging lens will form at the focal length.

so,

one position on optical axis is 2 cm to the right of converging lens

x = 2 cm ( right of converging lens)

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To find the second position, note that the image from lens become object for mirror, so object distance for mirror is 5 - 2 = 3 cm

so,

1/i = 1/f - 1/o

1/i = -1/1.5 - 1/3

i = - 1 cm

Therefore, second point is at 1 cm to the left of diverging mirror.

x = 1 cm ( left of diverging mirror)