A prism refracts a ray at two slanted faces, so the bends add instead of cancelling — the ray comes out turned by the deviation δ. Two clean relations run the whole story: r₁ + r₂ = A and δ = i₁ + i₂ − A. Swing the incidence and δ dips to a minimum; feed in white light and, because n depends on colour, the beam fans into a spectrum — and, in a raindrop, a rainbow.
Drag the incident ray onto the left face. It bends in (i₁ → r₁), crosses the glass, and bends out at the right face (r₂ → i₂). The two inside angles are locked to the apex by r₁ + r₂ = A, and the total turn is the deviation δ = i₁ + i₂ − A. Push the geometry until r₂ passes the critical angle and the exit face traps the ray entirely.
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Sweep the incidence and the deviation traces a valley: steep at grazing entry, steep again at grazing exit, with a single minimum δm in between. At that dip the ray passes symmetrically — i₁ = i₂, r₁ = r₂ = A/2, the ray inside running parallel to the base. That one measurement fixes the index. (shares the A and n set in §1)
Measure A and δm on the bench and this returns n directly — the standard way to grade an unknown glass.
The index isn't one number — it's larger for short wavelengths. So violet, seeing the biggest n, bends most and deviates most; red bends least. White light entering as one beam leaves as a spread spectrum, red at the top of the fan. Widen the apex to open the fan. (spread exaggerated for clarity)
Each colour obeys its own Snell's law with its own n. Newton's key insight: the prism doesn't colour the light — it merely sorts colours already present in white.
Cauchy’s relation. n drops smoothly as λ grows — so red (long λ) always sees the smallest n and bends least, violet the largest. A and B are constants of the glass; B sets how dispersive it is.
For a slim prism (A ≲ 10°) every sine collapses to its angle, and the messy formulae become one-liners that are independent of how the ray came in.
One turn for the whole prism — no dependence on incidence. A 5° crown prism (n = 1.5) deviates every ray by 2.5°.
The angular gap between the extreme colours — proportional to how much n changes across the spectrum.
A material constant (no A in it): crown ≈ 0.017, dense flint ≈ 0.033. Pair a crown and a flint and you can cancel one effect while keeping the other:
A raindrop is a tiny sphere that does what the prism does — refract, disperse, and (once) reflect off its back wall. Every drop sends each colour out at its own fixed angle from the incoming sunlight; you see a bow because only drops sitting on a 42° cone around the anti-solar point aim their light at your eye.
Sunlight enters the drop and disperses, reflects once off the far side, then exits and disperses again. The light piles up at a maximum bend — the 42° for red, 40° for violet.
Because red comes back at the larger angle, red rides the outer edge of the primary bow and violet the inner. The whole bow is just the set of drops at that special angle — which is why it's always a circle centred on your shadow's head.
A fainter secondary bow at 51° comes from drops that reflect twice — the extra bounce flips the order, so its colours run the other way.
Disperse light from a source and you get a spectrum — its wavelength composition laid out in space. What the spectrum looks like tells you what the source is made of. The instrument that produces a clean (pure) spectrum and measures its angles is the spectrometer.
All wavelengths present, blending smoothly. Hot dense solids/liquids — a bulb filament, molten iron.
Sharp bright lines at fixed λ on a dark ground — excited atoms. A fingerprint of the atom (e.g. sodium’s 589 nm doublet).
Groups of close lines fading into bands, sharp at one edge — excited molecules. Each band is a bunch of rotational lines.
Dark gaps where a cool gas swallowed those exact λ from a continuous background. The Sun’s Fraunhofer lines are these.
A pure spectrum needs a parallel beam in and a focusing lens out. The spectrometer supplies both around the prism, with a vernier circle to read every angle.
Slit at the focus of a lens → sends a parallel beam onto the prism.
Rotatable, levelled platform carrying the prism (or grating), turning with the circular scale.
Focused for parallel rays; swings on a vernier circle to catch each colour and read its angle.
A warm-up, an open bench where you steer a real prism into each condition and it checks you, then a JEE-Advanced / Olympiad exam bank. Collapse any rung you're done with.
Drag the incident ray, and slide the apex A and index n, until the prism satisfies each task — then hit check.
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