If we wanted to calculate the numerical position of an image or the focal length of a spherical mirror, we would use the mirror equation. It may be stated in one of these two alternative forms: In this equation each variable has a special meaning.
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do represents the distance from the vertex of the mirror to the position of the object as measured along the axis
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di represents the distance from the vertex of the mirror to the position of the image as measured along the axis
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f represents the focal length of the mirror. Remember that
2f = CV.
These sign conventions are summarized in the following table.
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do |
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positive
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when the object is "in front of the mirror"
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di |
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positive
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real images (inverted - "in front of the mirror")
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di |
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negative
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virtual images (upright - "behind the mirror")
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f
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positive
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converging (concave) mirrors
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f
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negative
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diverging (convex) mirrors
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In this equation, do, di, and f must be measured in the same unit - usually all three are either expressed in centimeters or in meters.
The formula used to calculate the magnification of an image is: where I and O represent the sizes of the image and object respectively.
As opposed to merely calculating the magnification of a mirror system, this equation is often used to compare the sizes of objects and images with their locations. For example, when a problem states that a real image is twice as large as an object this requires that you use the relationship
di = 2do in the mirror equation. A virtual image twice as large as the object would need you to use the value
di = -2do.
Let's work a few examples to show how these equations complement the ray diagrams that we have already learned how to construct. |