Light — Reflection & Refraction

Start simple: light bounces, and light bends

Look into a still pond. The sky sits mirrored on the surface — light bouncing straight back, which we call reflection — yet a stick poked into the water looks snapped at the waterline, because the light bends as it crosses in, which we call refraction. Both happen at the very same boundary between two clear materials. Reflection is the easy one: light leaves the surface at the same slant it arrived, just like a ball bouncing off a wall. The bending is the surprising one, and it happens for a simple reason — light travels at different speeds in different materials.

Build it up: how much does light bend?

Every transparent material gets a number called its refractive index $n$ — essentially "how much this material slows light down." Vacuum is exactly $n=1$, air is about $1.00$, water about $1.33$, ordinary glass about $1.5$. The larger $n$ is, the slower the light and the harder the ray bends. The bending is tied to the slant angles — always measured from the normal, the line pointing straight out of the surface — by Snell's law:

Quick number: a ray hits water from air at $\theta_1=30^\circ$. Then $\sin\theta_2=n_1\sin\theta_1/n_2=(1.00)(0.50)/1.33=0.376$, so $\theta_2\approx22^\circ$. The ray bent toward the normal because it slowed down entering the denser water.

Go deeper (AP / intro-college): trapped light and images

Run the logic backwards. Light leaving glass for air ($n_1>n_2$) bends away from the normal, and at a steep enough angle it cannot escape at all. Beyond the critical angle $\theta_c$, fixed by $\sin\theta_c=n_2/n_1$, every ray reflects entirely back inside — total internal reflection, the trick that pipes signals down a fibre-optic cable and makes a diamond sparkle. Curve the boundary instead of leaving it flat and the same bending focuses parallel rays to a point, described by the thin-lens equation $\tfrac{1}{f}=\tfrac{1}{d_o}+\tfrac{1}{d_i}$ with magnification $m=-d_i/d_o$. So a single idea — light changing speed at a boundary — quietly explains mirrors, lenses, fibres, cameras, and rainbows.

Try this in the simulation above

In 🌊 Refraction set $n_1=1.00$ and $n_2=1.33$, then drag the Incident angle up: the refracted ray bends more but always stays closer to the normal. Switch to 💎 Total Internal, set $n_1=1.50$ and $n_2=1.00$, and raise the angle past about $42^\circ$ — the refracted ray vanishes and the "Total Internal Reflection" flag lights up, matching $\sin\theta_c=1/1.5$. Finally, in 🔭 Lens/Mirror slide the Focal length and watch the image leap in position and flip over as $f$ passes the object distance.

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