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A plane (flat) mirror forms a virtual, upright, laterally reversed image that appears to be located as far behind the mirror as the object is in front of it. The image is virtual because the reflected rays diverge — they only appear to originate from behind the mirror and cannot be projected onto a screen. Ray diagrams are constructed by applying the law of reflection to at least two rays from each object point.
Draw ray diagrams for an object at various positions in front of a flat mirror. Verify that image distance equals object distance using a candle and a piece of glass as a two-way mirror.
The law of reflection — angle of incidence equals angle of reflection — is the only rule you need to construct a complete theory of plane mirrors. Start with a single point on an object, say the tip of an arrow. Draw two rays leaving that point and striking the mirror at different locations. Apply the law of reflection to each: the outgoing ray bounces away from the surface at the same angle it arrived, measured from the normal to the surface. The two reflected rays now travel away from the mirror in different directions. Your eye, receiving those two diverging rays, automatically traces them backward along straight lines into the mirror. Those backward-traced lines converge at a point *behind* the mirror — that convergence point is the image.
The geometry of this construction guarantees two things: the image is as far behind the mirror as the object is in front of it (image distance equals object distance), and the image is the same size as the object. The image is virtual because the rays do not actually pass through the image point — they only *appear* to diverge from it. A screen placed behind the mirror would catch no light there. This is the defining difference between a virtual image (apparent convergence of backward-traced rays) and a real image (actual convergence of forward-traveling rays).
The left-right reversal puzzle is worth resolving carefully. A plane mirror does not swap left and right; it swaps front and back — it maps the z-axis (depth) into its mirror while leaving x (horizontal) and y (vertical) unchanged. What you perceive as left-right reversal is actually a cognitive reinterpretation: you imagine *turning around* to face your image, and that mental rotation is what swaps left and right in your perception. Hold text up to a mirror and it appears reversed because you are mentally rotating it; hold it up to a window and look at the reflection from outside — same reversal, same reason. The mirror itself is indifferent to handedness in the horizontal sense.
Finally, the half-height rule: to see your full reflection you need a mirror of exactly half your height, mounted so its top is at halfway between your eyes and your head. This seems counterintuitive — surely walking closer would require a larger mirror? But because image distance equals object distance, both you and your image move closer together as you approach the mirror. The angle subtended stays constant. The minimum mirror size is fixed by your geometry, not your distance. This elegant result follows directly from the equal-angle reflection law applied to the extreme rays from your head and feet.