Prism — Part 2: Thin prisms, dispersion and the rainbow: visual lesson, ISC Class 12 Physics

Lesson

Thin Prisms, Dispersion and the Rainbow

Part 2 — a simple rule for thin prisms, why a prism spreads white light into colours, and how raindrops paint a rainbow.

In this lesson you will

Show that a thin prism deviates light by (n − 1)A and use it in air and in liquids
Explain dispersion and calculate angular dispersion and dispersive power
Explain, with a ray diagram, how raindrops form the primary rainbow

Concept

The thin prism: δ = (n − 1)A

For a thin prism (A a few degrees) and small angles of incidence, all the angles are small and $\sin\theta \approx \theta$ (in radians). Snell’s law becomes $i = n r_1$ and $e = n r_2$ , so $\delta = i + e - A = n(r_1 + r_2) - A = (n - 1)A$

The deviation does not depend on i (for small i): every ray is turned by the same angle.
δ is proportional to A and to (n − 1).

Diagram

How good is the thin-prism rule?

thin prism, A = 8°, n = 1.523 (exact)

For small angles of incidence δ ≈ (n − 1)A.

The exact deviation of an 8.0° prism (n = 1.523), traced with Snell’s law, compared with (n − 1)A:

Within about 1.5% of 4.18° for incidences up to about 12°.
At large angles of incidence the rule fails: the prism is then not "thin" for that ray.

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