8.3 Curved Mirrors

Notes

A concave (converging) mirror curves inward like a bowl; a convex (diverging) mirror bulges outward.

• Focal length $f$ is half the radius of curvature: $\displaystyle f = \frac{R}{2}$.
• Mirror equation: $\displaystyle \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$. Magnification $\displaystyle m = -\frac{d_i}{d_o}$.
• Sign rules: $f$ is positive for concave and negative for convex. A positive $d_i$ is a real image (in front of the mirror, inverted); a negative $d_i$ is virtual (behind the mirror, upright).
• A convex mirror always gives a smaller, upright, virtual image with a wide view (store security mirrors, car side mirrors).
• Example: concave mirror with $f = 10 \text{ cm}$, object at $30 \text{ cm}$: $\displaystyle \frac{1}{d_i} = \frac{1}{10} - \frac{1}{30} = \frac{2}{30}$, so $d_i = 15 \text{ cm}$ and $m = -0.5$.