Derive the expression for the deviation produced by a thin prism. Hence define dispersive power and show that it depends only on the material of the prism.

1. 1 · Use small angles. For a thin prism all the angles are small, so sin θ ≈ θ.
2. 2 · Apply Snell's law at both faces. i = μr₁ and e = μr₂, so i + e = μ(r₁ + r₂) = μA.
3. 3 · Combine with the prism relation. i + e = A + δ, so A + δ = μA, giving δ = (μ − 1)A.
4. 4 · Draw the diagram. [Thin prism with white light entering; red ray bent least and violet ray bent most; δr and δv marked]
5. 5 · Explain dispersion. μv > μr, so δv > δr; the angular dispersion is δv − δr = (μv − μr)A.
6. 6 · Define dispersive power. ω = (δv − δr)/δy = (μv − μr)/(μy − 1). A cancels, so ω depends only on the material.
7. 7 · Close in one line. So, a thin prism deviates light by (μ − 1)A, and its dispersive power is a property of its glass.

Scoring tip: Show A cancelling in the last step; that is what proves ω does not depend on the prism angle.