Draw a labelled ray diagram for refraction through a prism. Derive the relation between the refractive index, the angle of the prism and the angle of minimum deviation, and draw the i-δ graph.

1. 1 · State what happens. A prism bends light towards its base through an angle of deviation δ, which is least when the ray passes symmetrically.
2. 2 · Draw the ray diagram. [Prism ABC; incident ray PQ, refracted ray QR and emergent ray RS; normals meeting at O; mark i, r₁, r₂, e, A and δ]
3. 3 · Show that r₁ + r₂ = A.
   • Quadrilateral AQOR: A + ∠QOR = 180°
   • Triangle QOR: r₁ + r₂ + ∠QOR = 180°
   • So r₁ + r₂ = A
4. 4 · Show that i + e = A + δ. δ = (i − r₁) + (e − r₂) = i + e − A.
5. 5 · Apply minimum deviation.
   • i = e and r₁ = r₂ = r, so r = A/2
   • 2i = A + δm, so i = (A + δm)/2
6. 6 · Use Snell's law. μ = sin i / sin r = sin[(A + δm)/2] / sin(A/2).
7. 7 · Draw the graph. [δ on the y-axis against i on the x-axis: a U-shaped curve with its lowest point marked δm]
8. 8 · Close in one line. So, measuring A and δm for a prism gives the refractive index of its material.

Scoring tip: Draw the normals as dotted lines and mark all six angles. Label both axes of the graph.