4. An observer to the right of a mirror-lens combination shown below sees two re

Question

4. An observer to the right of a mirror-lens combination shown below sees two real images that are the same size and in the same location (one image is formed by the light from the object passing through only the lens, the other image is formed from the light first being reflected by the mirror, and then passing through the lens). One image is upright, and the other is inverted. Both images are 1.50 times larger than the object. The lens has a focal length of 10.0 cm. The lens and mirror are seperated by 40.0 cm. Determine the focal length of the mirror. (DON

Explanation / Answer

(mirror)------(object)-------(lens)-----...
fm=? fl=10 M= 1.50

In order for the two images to be the exact same thing, but inverted, we know that the image produced by the mirror needs to be in the exact same place as the object, but inverted.

For the lens:
M = -1.50 = -q/p
q= 1.50p

1/p + 1/q = 1/f
1/p + 1/1.50p = 1/10
p = 16.7 cm
This is the distance of the object from the lens.
Since the mirror is 40cm away from the lens, the object is (40-16.7) 23.3 cm away from the mirror.

Using the reasoning I described above, for the mirror p=q
So,
1/23.3 + 1/23.3 = 1/f

f=11.7 cm

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