Two converging lenses of unequal focal lengths can be used to reduce the aperture of a parallel beam of light without loosing the energy of the light. This increase the intensity. Describe how the converging lenses should be placed to do this.
Answers
It can be achieved by placing the larger focal length lens towards the incoming beam and then the smaller focal length lens at a distance f+f' from the first lens. See the diagram below. In the above diagram, the focal length of the lens AB = f and the focal length of the lens CD = f', such that f > f'. The aperture of the incoming parallel beam is AB. The first lens converges it at the point F, PF = f. Since F is also the focal point of the lens CD, the rays coming from F become a parallel beam of aperture CD after passing through the second lens. The energy of the beam remains the same after passing through the two lenses. The triangle APF and FP'D are similar triangles hence PF/P'F =AP/DP' =2AP/2DP' =AB/CD →AB/CD =PF/P'F = f/f' Since f > f', AB > CD So the aperture is reduced by this arrangement. The intensity is the energy per unit area. The energy of the light beam is constant but aperture (hence the area) reduces, thus intensity increases in this process.
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