PhysicsLAB Resource Lesson
Mirror Equation

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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.
  • do represents the distance from the vertex of the mirror to the position of the object as measured along the axis
  • di represents the distance from the vertex of the mirror to the position of the image as measured along the axis
  • f represents the focal length of the mirror. Remember that 2f = CV.
These sign conventions are summarized in the following table.
do   positive   when the object is "in front of the mirror"
di   positive   real images (inverted - "in front of the mirror")
di   negative   virtual images (upright - "behind the mirror")
f   positive   converging (concave) mirrors
f   negative   diverging (convex) mirrors

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.
Refer to the following information for the next seven questions.

A candle is placed 30 cm in front of a concave mirror that has a radius of curvature of 15 cm.
 What type of image will be formed, real or virtual?

 Which of these properties will the image manifest: upright/inverted? enlarged/equal/reduced in size?

 Where will the image be formed?

 If the candle is 35 cm tall, then how tall is its image?

 If the mirror were changed to a convex mirror with the same radius of curvature, what properties would the new image manifest: real/virtual? upright/inverted? enlarged/equal/reduced in size?

 Where would the new image be formed?

 How tall is this second image?

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