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An 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 is unavoidable. To see why, consider the mathematical approximation we’ve been making, which is that the depth of the mirror’s curve is small compared to do and di. Since only a flat mirror can satisfy this shallow-mirror condition perfectly, any curved mirror will deviate somewhat from the mathematical behavior we derived by assuming that condition.

Dividing by infinity gives zero, so we have 1/do = –1/di , or do = –di . If we interpret the minus sign as indicating a virtual image on the far side of the mirror from the object, this makes sense. It turns out that for any of the six possible combinations of real or virtual images formed by inbending or out-bending lenses or mirrors, we can apply equations of the form θf = θi+θo and 1 f = 1 + 1 di do , with only a modification of plus or minus signs. There are two possible approaches here. The approach we have been using so far is the more popular approach in textbooks: leave the equation the same, but attach interpretations to the resulting negative or positive values of the variables.

Even though the spherical mirror (solid line) is not well adapted for viewing an object at infinity, we can improve its performance greatly by stopping it down. Now the only part of the mirror being used is the central portion, where its shape is virtually indistinguishable from a parabola (dashed line). 44 Chapter 3 Images by Reflection, Part II Summary Selected Vocabulary focal length........................ a property of a lens or mirror, equal to the distance from the lens or mirror to the image it forms of an object that is infinitely far away Notation f .........................................

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