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Lesson 3.9 • Competency 3.9Complete Lesson
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Refraction of Light, Lenses and Prisms

Snell’s law of refraction n₁ sin θ₁ = n₂ sin θ₂, critical angle and total internal reflection, real and apparent depth, minimum deviation in triangular prisms, thin lenses, and lens formula 1/v - 1/u = 1/f.

Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.

Learning Objectives

  • Apply Snell’s law to calculate angles of refraction, critical angles, and lateral displacement across plane boundaries.
  • Derive and solve problems involving prism minimum deviation n = sin((A + Dm)/2) / sin(A/2) and thin lens formulas.

Core Theory & Concepts

Refraction is the change in the direction of propagation of a light ray when crossing the interface between two optical media of different wave speeds, governing prisms, lenses, and optical fibres.

Snell’s Law & Critical Angle

For light entering medium 2 from medium 1: n₁ sin θ₁ = n₂ sin θ₂. When passing from dense to rare medium, total internal reflection occurs if incident angle θ₁ > C, where sin C = n₂/n₁.

n_1 \sin \theta_1 = n_2 \sin \theta_2, \quad \sin C = \frac{1}{n}

Prism Minimum Deviation Formula

At minimum deviation Dm, the ray passes symmetrically through the prism (i₁ = i₂ and r₁ = r₂ = A/2). Refractive index is n = sin((A + Dm)/2) / sin(A/2).

n = \frac{\sin\left(\frac{A + D_m}{2}\right)}{\sin\left(\frac{A}{2}\right)}

Common Misconceptions

Misconception

Total internal reflection can occur when light travels from air into glass.

Physical Clarification:Total internal reflection is physically possible ONLY when light travels from an optically denser medium toward an optically rarer medium (n₁ > n₂).

Syllabus Topic Outline

Competency 3.9
  • 1Laws of refraction and absolute refractive index n = c/v
  • 2Critical angle C: sin C = 1/n and total internal reflection
  • 3Real and apparent depth: apparent depth = real depth / n
  • 4Prism deviation angle d = i₁ + i₂ - A and minimum deviation Dm
  • 5Thin lens formula: 1/v - 1/u = 1/f (Cartesian sign convention)
  • 6Linear magnification m = v/u and lens power P = 1/f (Dioptres)

Practice Problems