Simple Nature - Light and Matter

h / A diverging mirror in the shapeof a sphere. The image is reduced(M < 1). This is similarto example 8, but here the imageis distorted because the mirror’scurve is not shallow.A shortcut for real images example 9In the case of a real image, there is a shortcut for step 1, thedetermination of the signs. In a real image, the rays cross atboth the object and the image. We can therefore time-reverse theray diagram, so that all the rays are coming from the image andreconverging at the object. Object and image swap roles. Dueto this time-reversal symmetry, the object and image cannot betreated differently in any of the equations, and they must thereforehave the same signs. They are both positive, since they must addup to a positive result.12.3.3 ⋆ AberrationsAn imperfection or distortion in an image is called an aberration.An aberration can be produced by a flaw in a lens or mirror,but even with a perfect optical surface some degree of aberration isunavoidable. To see why, consider the mathematical approximationwe’ve been making, which is that the depth of the mirror’s curveis small compared to d o and d i . Since only a flat mirror can satisfythis shallow-mirror condition perfectly, any curved mirror willdeviate somewhat from the mathematical behavior we derived byassuming that condition. There are two main types of aberration incurved mirrors, and these also occur with lenses.(1) An object on the axis of the lens or mirror may be imagedcorrectly, but off-axis objects may be out of focus or distorted. Ina camera, this type of aberration would show up as a fuzziness orwarping near the sides of the picture when the center was perfectlyfocused. An example of this is shown in figure i, and in that particularexample, the aberration is not a sign that the equipment wasof low quality or wasn’t right for the job but rather an inevitableresult of trying to flatten a panoramic view; in the limit of a 360-766 Chapter 12 Optics