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. Draw the i-δ graph.
How to lay out the answer. Follow the frame, then write it in your own words.
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 · Draw the ray diagram. [Prism ABC; incident ray PQ, refracted ray QR and emergent ray RS; normals meeting at N; mark i, r₁, r₂, e, A and δ]
3 · Show that r₁ + r₂ = A.
Quadrilateral AQNR: A + ∠QNR = 180°
Triangle QNR: r₁ + r₂ + ∠QNR = 180°
So r₁ + r₂ = A
4 · Show that A + δ = i + e. δ = (i − r₁) + (e − r₂) = i + e − A.
5 · Apply minimum deviation.
i = e and r₁ = r₂ = r, so r = A/2
A + Dm = 2i, so i = (A + Dm)/2
6 · Use Snell's law. n = sin i / sin r = sin[(A + Dm)/2] / sin(A/2).
7 · Draw the graph. [δ on the y-axis against i on the x-axis: a U-shaped curve with its lowest point marked Dm]
8 · Close in one line. Measuring A and Dm 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.
