Light
Section: Waves | Syllabus: Cambridge AS Level Physics 9702
Light is a transverse electromagnetic wave that travels at 3 × 10⁸ m/s in a vacuum. It travels in straight lines and can pass through transparent materials like glass and water. Reflection of Light Light follows the same reflection rules as all waves (see Wave Behaviour).
The law of reflection states: angle of incidence (i) = angle of reflection (r) , both measured from the normal. Plane Mirror Images A plane (flat) mirror forms images with specific characteristics: Plane Mirror Image Characteristics Same size as the object Same distance behind the mirror as the object is in front Virtual (cannot be projected onto a screen) Laterally inverted (left and right are swapped) Upright (same way up as object) Refraction of Light Light refracts (bends) when passing between media due to speed changes.
The rules covered in Wave Behaviour apply: light bends toward the normal when slowing down (entering denser medium) and away when speeding up. Frequency never changes during refraction. Speed of Light in Different Media Medium Approximate Speed Vacuum 3.0 × 10⁸ m/s Water 2.25 × 10⁸ m/s Glass 2.0 × 10⁸ m/s Diamond 1.24 × 10⁸ m/s Example: Pencil in Water A pencil in water appears bent at the surface because light refracts as it exits the water into air.
Refractive Index The refractive index is a number that describes how much a material slows down light compared to a vacuum. It's a fundamental property of every transparent material. Definition of Refractive Index n = c/v Where: \(n\) = refractive index (no units) \(c\) = speed of light in vacuum (\(3.0 × 10^8\) m/s) \(v\) = speed of light in the material (m/s) Understanding Refractive Index What it tells us: How much slower light travels in a material compared to a vacuum How much light will bend when entering/leaving the material The optical density of the material Key points: Refractive index is always ≥ 1 (light is fastest in vacuum) Higher refractive index = more optical dense = light slower = more bending Lower refractive index = less optically dense = light faster = less bending Refractive index has no units (it's a ratio) Refractive Indices of Common Materials Material Refractive Index (n) Optical Density Vacuum 1.00 (exactly) Lowest (reference) Air 1.0003 (≈ 1.00) Very low Water 1.33 Medium Glass (typical) 1.5 Medium-high Perspex 1.49 Medium-high Diamond 2.42 Very high Quick Interpretation: A refractive index of 1.5 means light travels 1.5 times slower in that material than in a vacuum.
Snell's Law Snell's Law is the mathematical relationship that precisely describes refraction: Snell's Law n_1 i = n_2 r Where: \(n_1\) = refractive index of first medium \(n_2\) = refractive index of second medium \(i\) = angle of incidence \(r\) = angle of refraction Alternative forms: For light going from air (n ≈ 1) into a material: sin i / sin r = n This simplifies to: n = sin i / sin r (when n₁ = 1) Example: Using Snell's Law Question: Light enters glass (n = 1.5) from air at an angle of 40° to the normal.
Calculate the angle of refraction. Solution Given: n₁ = 1.0 (air), n₂ = 1.5 (glass), i = 40° n₁ sin i = n₂ sin r 1.0 × sin 40° = 1.5 × sin r sin r = 0.643 / 1.5 = 0.429 r = sin⁻¹(0.429) = 25.4° Critical Angle Connection The refractive index determines the critical angle for total internal reflection: C = 1/n Where: \(C\) = critical angle \(n\) = refractive index of the denser medium (relative to air) Key relationship: Higher refractive index → smaller critical angle Diamond (n = 2.42) has critical angle of ~24.4° Glass (n = 1.5) has critical angle of ~42° Water (n = 1.33) has critical angle of ~49° Exam Tips for Refractive Index: Always write the formula first: n = c / v or n₁ sin i = n₂ sin r Refractive index has no units Check your calculator is in degree mode for Snell's Law Higher n means more bending toward normal when entering Show all working steps-marks are awarded even if final answer is wrong Remember: n is always ≥ 1 Total Internal Reflection Total Internal Reflection (TIR) occurs when light traveling in a denser medium hits the boundary with a less dense medium at an angle greater than the critical angle, causing all light to reflect back into the denser medium.
Key Concept: Total internal reflection is not just reflection-it's a special case where 100% of light is reflected with no refraction occurring. This creates perfect, lossless reflection. Conditions for Total Internal Reflection For TIR to occur, TWO conditions must be met: Light must travel from a more dense to a less dense medium E.g., glass → air, water → air, glass → water NOT air → glass (this is wrong direction!) The angle of incidence must be greater than the critical angle If i > C → Total internal reflection occurs If i = C → Light travels along the boundary If i Common Mistake: Students often forget that TIR only happens when going from dense → less dense.
It's impossible when going from less dense → more dense (like air → water). The Critical Angle The critical angle (C) is the angle of inc…
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