Question

5.50* Two positive lenses are to be used as a laserbeam expander. An axial 1.0-mm-diameter beam enters a short focal length positive lens, which is followed by a somewhat longer focal length positive lens from which it emerges with a diameter of 8.0 mm. Given that the first lens has a 50.0 mm focal length, determine the focal length of the second lens and the separation between the lenses. Draw a diagram

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The rule is that the ratio of the focal lengths is equal to these ratio of the beam expansion that is, In order to re colimate the beam, the second lens has to be positioned faraway from this focus.

The two triangles formed are similar and hence the ratio of the beam diameter equal the ratio of the focal lengths the two lenses are therefore a distance apart.

The ratio of diameter is 8 - therefore the second lenses has a focal length of 8 x 50mm = 400mm, and the distance between the two is 450mm.

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