A textbook shows you one frozen ray diagram and moves on. Here you move the light — grab any ray, mirror, or object and drag it, and watch the geometry keep the laws true. Where a proof matters, press play and the steps draw themselves on the figure. Read slowly; the payoff is that spherical mirrors will feel like nothing new.
The law i = r holds at every point of every surface. Drag the light source and watch: on the polished surface the beam stays organised (an image forms); on the rough one every facet has its own normal, so the same law scatters the beam and you just see the surface.
Key idea. Reflection is not a special property of mirrors. It is the same law everywhere — a mirror is just smooth enough to keep the geometry intact. A rough page scatters light so you can read it from any angle.
The angle of incidence equals the angle of reflection, ∠i = ∠r — both measured from the normal, the perpendicular to the surface at the point where the ray lands.
The incident ray, the reflected ray and the normal all lie in one plane. The reflected ray never swings sideways out of it.
Why the normal? It is the one direction the surface itself defines. On a curved mirror there's no single "surface line", but there is always a normal — so the same two laws carry over to concave and convex mirrors in Part II.
Hold the incident ray fixed and rotate the mirror. Because the reflected ray is fixed by the normal, and the normal turns with the mirror by θ, the reflected ray swings by twice as much. Grab the mirror and feel it — then press play to see why.
A mirror scanner spins at 300 rev/s. How fast does the reflected beam sweep?
Twice the mirror rate: 2 × 300 = 600 rev/s. This doubling is exactly what makes mirror-galvanometer readouts so sensitive.
Drag the object O. Two rays leave it, reflect with i = r, and diverge — they never meet. Traced back (dashed) they meet at one point O′ behind the glass, and that is what your eye sees. Press play to watch the construction build, then prove O′ sits exactly as far behind as O is in front.
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Drag the object and notice: the image moves the same way vertically, but mirror-opposite horizontally. A mirror doesn't swap left and right — it swaps front and back. Every point maps straight through the glass to an equal depth behind.
Left and right only seem swapped because you mentally turn around to compare — and turning around is itself a left-right flip. That is why the letter R lands mirror-formed.
Printed reversed on the bonnet, the word passes through the driver-ahead's rear-view mirror and lands the right way round.
Each mirror images the object; each image is then imaged by the other, and so on. They all land on a circle centred where the mirrors meet. Counting them gives a clean rule.
If 360/θ is even → exactly (360/θ − 1) images, wherever the object sits.
If 360/θ is odd → (360/θ − 1) on the bisector, else 360/θ. Drag the dot off-centre and watch the count tick up. Parallel mirrors (θ → 0) give infinitely many.
Drag the object O. Its image O′ stays exactly as far behind as O is in front, and the shaded wedge is every place your eye could sit and still catch O′ in this finite mirror.
Ready for curved glass? The Workbench is the full 2D ⇄ 3D bench — plane, concave and convex — where you drag the object through every case and read u · v · f · m live.
Three ladders. A quick warm-up, then an open laboratory where the questions ask you to build the setup and the bench checks you, then an exam bank of JEE / AP-grade problems. Collapse any rung you're done with — tap its title bar.
This bench is yours. Switch between one plane mirror and two inclined mirrors, set the angle, and drag the object. Each task names a configuration — recreate it, then hit check the setup. Shuffle for a fresh order any time.
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