Mirrors
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 5 practice questions.
A concave mirror curves inward and focuses light (f > 0). A convex mirror bulges outward and spreads it (f < 0). Both follow 1/so + 1/si = 1/f and M = −si/so, with f = R/2.
1. Ray diagrams
2. What a concave mirror does
Rays to draw: parallel to the axis → reflects through F. Through F → reflects parallel. To the center of curvature C → reflects straight back.
A convex mirror always gives a virtual, upright, smaller image, which shows a wide view. That’s why it’s used for security and car side mirrors.
3. Example, then try it
An object is 45 cm from a concave mirror with f = 15 cm. Find the image.
1/si = 1/15 − 1/45 = 2/45, so si = 22.5 cm (real, in front).
M = −22.5/45 = −0.50: inverted and half the size.
You hold your face 10 cm from a concave makeup mirror with f = 20 cm. Describe your image. Then a shopper stands 2.0 m from a convex security mirror with f = −0.50 m. Describe their image.
Makeup mirror: 1/si = 1/20 − 1/10 = −1/20, so si = −20 cm: virtual, behind the mirror.
Magnification: M = −(−20)/10 = +2: upright and twice as large.
Security mirror: 1/si = 1/(−0.50) − 1/2.0 = −2.5, so si = −0.40 m: virtual.
Magnification: M = −(−0.40)/2.0 = +0.20: upright and one-fifth the size.
Answer: makeup mirror: virtual, upright, 2×; security mirror: virtual, upright, 0.20×.
4. Common mistakes
An object is placed exactly at the focal point of a concave mirror. Where is the image?
1/si = 1/f − 1/f = 0, so si is infinite. The reflected rays leave parallel and never meet.
Ready to practice?
5 questions on Mirrors, each with a hint and an explanation for every wrong answer.