IGCSE CP4c – Triangular Prism | Edexcel International GCSE Physics

Theory — Prism and Dispersion

A triangular prism refracts light twice — once entering, once leaving — bending it toward the base.

Four Angles

All angles are measured from the normal to the surface. There are four angles in a prism refraction:

θ₁ — angle of incidence at face 1 (in air, outside prism)
θ₂ — angle of refraction at face 1 (inside glass)
θ₃ — angle of incidence at face 2 (inside glass) = A − θ₂
θ₄ — angle of refraction at face 2 (in air, outside prism)

sin θ₁ = n sin θ₂ (Snell's Law, air→glass) θ₃ = A − θ₂ (geometry, A = 60°) n sin θ₃ = sin θ₄ (Snell's Law, glass→air) δ = θ₁ + θ₄ − A (angle of deviation)

Dispersion

Glass has a slightly different refractive index for each wavelength. Violet light (high n) bends more than red light (low n), so white light splits into a spectrum — violet closest to the base, red furthest.

Procedure

Equipment

Equilateral glass prism (A=60°) · Ray box · White light + colour filters · Plain paper · Protractor · Ruler · Darkened room

1

Outline the prism and mark entry point

Place prism on paper, draw around it. Mark entry point on left face, draw normal at that point.

2

Shine ray and mark both rays

Aim ray box at entry point at chosen θ₁. Mark incident ray (two dots, left side) and emergent ray (two dots, right side).

💡 The ray inside the glass is invisible — mark only incident and emergent rays directly.

3

Complete ray path and measure all four angles

Remove prism. Draw incident and emergent rays, connect entry and exit points for internal ray. Draw normals at both faces. Measure θ₁, θ₂, θ₃, θ₄ from their normals.

4

White light — see dispersion

Use white light source. Emergent beam spreads into a spectrum. Hold white card on exit side.

💡 Violet is closest to the apex (most deviated), red is furthest.

🌈 Select a light source and adjust θ₁ with the slider. Angle arcs show θ₁–θ₄ from their normals. Switch to White Light to see dispersion.

Light Source

Angle of Incidence θ₁

θ₁ 40°

25°70°

Angles

θ₁ (face 1, air)40°

θ₂ (face 1, glass)—

θ₃ (face 2, glass)—

θ₄ (face 2, air)—

δ = θ₁+θ₄−60°—

Min deviation at—

Questions

Question 1

A ray enters an equilateral prism (A=60°, n=1.52) at θ₁=45°. Calculate θ₂, θ₃, θ₄ and the deviation δ. Show all steps.

Step 1 — θ₂: sin θ₂ = sin 45°/1.52 = 0.4652 → θ₂ = 27.7°. Step 2 — θ₃ = A−θ₂ = 60°−27.7° = 32.3°. Step 3 — θ₄: sin θ₄ = 1.52 × sin 32.3° = 0.8129 → θ₄ = 54.4°. Step 4 — δ = 45°+54.4°−60° = 39.4°.

Question 2

Explain why white light disperses into a spectrum through a prism. List colours from least to most deviated.

White light is a mixture of all visible wavelengths. Glass has a slightly different refractive index n for each wavelength (dispersion) — shorter wavelengths have a higher n. Each colour therefore refracts by a different amount, emerging at a different angle. Order least to most deviated: red → orange → yellow → green → blue → violet.

Question 3

What is minimum deviation? At minimum deviation, what is the relationship between θ₁ and θ₄, and what can you say about the ray path inside the prism?

Minimum deviation is the smallest angle of deviation for a given prism and wavelength. At minimum deviation: θ₁ = θ₄ (the prism is used symmetrically); θ₂ = θ₃ = A/2 = 30°; and the ray inside the prism travels parallel to the base. As θ₁ increases from its minimum possible value, δ first decreases, reaches δ_min, then increases again.