Cross a boundary at an angle and light changes speed — so it changes direction. One line, n₁ sin θ₁ = n₂ sin θ₂, runs through everything here: the bent straw, the shallow-looking pool, the sparkle of a diamond, the internet in a glass thread. Grab a ray and drag it; the geometry keeps Snell's law true.
Set the index on both sides and drag the incident ray. Into a denser medium (n₂ > n₁) the ray bends toward the normal; the other way it bends away and the pencil diverges — push it far enough and nothing gets through at all. Across the boundary the product n·sin θ always matches.
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A slab bends the ray twice, equal and opposite, so it emerges parallel to how it went in — just nudged sideways. That nudge is the lateral shift. Drag the ray and watch the shift grow with the angle.
Formula. d = t · sin(θ₁ − θ₂) / cos θ₂, with thickness t = 3.0 units. For small angles this collapses to d ≈ t·θ₁·(1 − 1/n).
Rays from the object bend at the surface and, traced back, seem to start somewhere else — so a submerged object never looks where it truly is. Which way it shifts depends on which side is denser. Here are the terms and the law; then drag the object to watch them move.
A fish in water seen from the air: the image rises toward the surface, dapp < dreal.
A bird in air seen from under the water: the image lifts farther, dapp > dreal.
Δt is the apparent displacement — the gap between where the object is and where it appears.
Both follow from Snell near the normal. A coin under a glass block rises by t(1 − 1/n); a fish appears higher to a diver looking down its own reflection.
Now go the other way — dense to rare, so the ray bends away from the normal. Widen the angle and the refracted ray swings flatter until, at the critical angle, it grazes the surface. Past it, none escapes: the boundary becomes a perfect mirror.
θc = sin⁻¹(1/n). Denser glass → smaller critical angle → easier to trap light. A diamond's tiny 24.4° is why it holds fire.
Bend the trapping into a thread. As long as every bounce hits the wall beyond the critical angle, the ray never leaks — it ricochets down the core for kilometres. Steepen the launch too far and it spills out. Drag the launch to feel the edge.
The core here has n = 1.50, so θc ≈ 41.8°. Rays launched close to the axis strike the wall near-grazing (large incidence) and stay locked in. That steep-vs-shallow limit is captured by the fibre's numerical aperture.
Snell's law fires again at every boundary. Stack layers of rising index and the ray bends a little more at each — a staircase leaning toward the vertical. Let the layers grow infinitely thin and the staircase smooths into a curve: that continuous version is a mirage, the flattened setting Sun, the twinkle of a star.
Because n·sin θ is conserved layer to layer, the ray keeps turning the same way. Reverse the gradient — hot, thin air near a road below cooler air — and it curves the other way, lifting a shimmering "puddle" of sky: a mirage.
On a baking road the air right at the surface is hot and thin — a lower index than the cooler air above. That is the gradient flipped: index now rises with height.
A near-horizontal ray from the sky dips toward the road, and by n·sin θ = constant it keeps bending until it turns horizontal and curves back up into your eye — an upside-down total-reflection near the ground.
Your brain traces that arriving ray straight backward, placing an image of the sky below the road. That inverted patch of shimmering sky is what looks like a pool of water — the same physics flattens the setting Sun and makes stars twinkle.
A warm-up, an open bench where you build the condition and it checks you, then a JEE-grade exam bank. Collapse any rung you're done with.
Light rises from glass into air. Drag the ray to set the angle inside, slide the glass index, and recreate each task, then hit check.
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