Question
Mon January 09, 2012 By:
 

derive the mirror equation

Expert Reply
Tue January 10, 2012

Sign convention and symbols
We use the same sign convention and symbols that we use with lenses to refer to the principle points of curved mirrors. This simplifies the mathematical equations.

By tracing the principle rays, we see pairs of similar triangles.

Mirror equation:
Using the similar triangles GHF and VEF:

Equation 1

and similar triangles ABV and GHV:

Equation 2

Since AB = EV, then

We can combine Equations 1 and 2:

Divide both sides by di:

and rearrange, giving us the Mirror Equation:

 

Magnification Equation:
Using similar triangles ABV and GHV again:

By assigning a negative value to the inverted image, we have the Magnification Equation

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