Using the small-angle approximation, the angles α, α′, and ϕabove can be replaced by their tangents, yielding
Note that we have neglected the axial distance VQ, small when ϕ is small. Cancellation of h produces the desired relationship,
If the spherical surface is chosen to be concave instead, the center of curvature will be to the left. For certain positions of the object point O, it is then possible to find a real image point, also to the left of the mirror. In these cases, the resulting geometric relationship analogous to Equation 3-5 consists of the same terms, but with different algebraic signs, depending on the sign convention employed. We can choose a sign convention that leads to a single equation, the mirror equation, valid for both types of mirrors. It is Equation 3-6.
2. Sign convention. The sign convention to be used in conjunction with Equation 3-6 and Figure 3-18 is as follows.
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