When the sign convention is taken into account, one has, for the general case, a single equation, Equation 3-7, valid for both convex and concave mirrors.

If, after calculation, the value of m is positive, the image is erect. If the value is negative, the image is inverted.

Let us now use the mirror formulas in Equations 3-6 and 3-7, and the sign convention, to locate an image and determine its size.

Example 7

A meterstick lies along the optical axis of a convex mirror of focal length 40 cm, with its near end 60 cm from the mirror surface. Five-centimeter toy figures stand erect on both the near and far ends of the meterstick. (a) How long is the virtual image of the meterstick? (b) How tall are the toy figures in the image, and are they erect or inverted?

Solution: Use the mirror equationtwice, once for the near end and once for the far

end of the meterstick. Use the magnification equationfor each toy figure.