Curved Mirrors, the Mirror Equation and Real Images
A concave mirror brings parallel light to a focus at half its radius of curvature, and one equation then locates the image for any object distance. Sign conventions decide whether the image is real or virtual, upright or inverted, and they are where most of the difficulty sits.
What a learner can do afterwards
- Locates an image by ray construction for concave and convex mirrors and checks it against the mirror equation
- Relates focal length to radius of curvature and explains why a spherical mirror blurs light far off axis
- Explains why a shaving mirror magnifies while a car wing mirror shrinks the view and widens it
1 · Read
A spherical mirror is a polished slice of a sphere: concave when the inside shines, convex when the outside does. Rays parallel to the axis meet nearly at the focal point halfway between mirror and centre, so focal length is half the radius. Three principal rays locate any image: parallel then through focus, through focus then parallel, and straight at the centre. A mirror of radius 20 cm focuses at 10 cm.
Concave mirrors magnify when your face sits inside the focal length, which is why shaving mirrors enlarge. The reflected rays only appear to meet behind the glass, giving a virtual upright image. Move beyond focus and the image flips to real and inverted, projectable onto a screen. Convex mirrors do the opposite: they shrink the view upright and virtual, widening the field the way car wing mirrors do.
The mirror equation links object distance, image distance, and focal length. Sign conventions decide whether the image is real or virtual, upright or inverted, and they are where most of the difficulty sits. Always check the ray construction against the equation: agreement means the signs are right.
Spherical mirrors blur light that strikes far from the axis, since those rays miss the shared focus. This spherical aberration grows with aperture, so wide fast mirrors need correction. Parabolic figures fix it by design, bringing parallel rays to a single point, which is why telescope primaries are paraboloids. Know the failure mode and you know when the mirror equation is enough.
Focus at half the radius, rays for the picture, signs for the verdict, parabolas for wide sharp mirrors.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.