FORMULA CHAPTER
Chapter 04 – Refraction of Light at Plane Surfaces
Refractive Index from Apparent Depth
Worked example
Given: real depth = 12 cm, apparent depth = 8 cm Calculation: μ = 12 / 8 Answer: μ = 1.5
Absolute Refractive Index
Worked example
Given: c = 3 × 10⁸ m/s, v = 2 × 10⁸ m/s Calculation: μ = 3 / 2 Answer: μ = 1.5
Relative Refractive Index
Worked example
Given: μ₁ = 1.0, μ₂ = 1.5 Calculation: μ₁₂ = 1.5 / 1.0 Answer: μ₁₂ = 1.5
Reciprocal Refractive Indices
Worked example
Given: μ₁₂ = 1.5 Calculation: μ₂₁ = 1 / 1.5 Answer: μ₂₁ ≈ 0.67
Prism Deviation
Worked example
Given: i₁ = 45°, i₂ = 45°, r₁ = 30°, r₂ = 30° Calculation: δ = 90° − 60° Answer: δ = 30°
Prism Angle Relation
Worked example
Given: r₁ = 25°, r₂ = 35° Calculation: A = 25° + 35° Answer: A = 60°
Minimum Deviation Relation
Worked example
Given: i = 48°, A = 60° Calculation: δmin = 96° − 60° Answer: δmin = 36°
Refractive Index from Angles
Worked example
Given: i = 45°, r = 28° Calculation: μ = sin 45° / sin 28° Answer: μ ≈ 1.51
Apparent Upward Shift
Worked example
Given: real depth = 12 cm, μ = 1.5 Calculation: Shift = 12 × (1 − 1/1.5) Answer: Shift = 4 cm
Refractive Index from Critical Angle
Worked example
Given: C = 42° Calculation: μ = 1 / sin 42° Answer: μ ≈ 1.49
Wave Equation
Worked example
Given: f = 500 Hz, wavelength = 0.68 m Calculation: v = 500 × 0.68 Answer: v = 340 m/s