Have you ever noticed how a straw appears to bend when placed in a glass of water? Or why a swimming pool looks shallower than it actually is? Or why a diamond sparkles with such extraordinary brilliance? All of these everyday phenomena are caused by the same physical principle: refraction of light — the bending of light as it passes from one transparent medium to another.
Refraction occurs because light travels at different speeds in different media. In vacuum, light travels at c = 3×10&sup8; m/s — the fastest possible speed in the universe. In glass, it slows to about 2×10&sup8; m/s; in water, to 2.25×10&sup8; m/s. This change in speed causes the light ray to change direction at the boundary between two media, a behaviour mathematically described by Snell’s Law.
Refraction is not just a curiosity — it is the operating principle behind eyeglasses, cameras, telescopes, microscopes, optical fibres, endoscopes, and medical imaging. Every lens ever made uses refraction to focus or diverge light. For CBSE Class 10 Physics Chapter 10 (Light — Reflection and Refraction) and CBSE Class 12 Physics Chapter 9 (Ray Optics and Optical Instruments), refraction is a core topic appearing in every board examination. This guide covers all key subtopics with derivations, diagrams, applications, and five CBSE exam-ready solved problems.
- 1. Laws of Refraction
- 2. Refractive Index — Absolute and Relative
- 3. Refraction Through a Glass Slab — Lateral Displacement
- 4. Real and Apparent Depth
- 5. Total Internal Reflection (TIR) and Critical Angle
- 6. Applications of Total Internal Reflection
- 7. Real-Life Examples of Refraction
- 8. Solved Numerical Problems
- 9. Frequently Asked Questions (FAQ)
1. Laws of Refraction
When a ray of light passes from one transparent medium to another, it changes both speed and direction (unless it strikes the surface at 90°, i.e., normal incidence). There are two laws that govern refraction:
Equivalently: n₁ sinθ₁ = n₂ sinθ₂
Named after Dutch mathematician Willebrord Snell (1621), though Descartes published it independently.
2. Refractive Index — Absolute and Relative
n = c/v, where c = 3×10&sup8; m/s (speed of light in vacuum), v = speed of light in the medium.
Key properties:
• n is always ≥ 1 (light is always slower in a medium than in vacuum).
• For vacuum: n = 1 (exactly). For air: n ≈ 1.0003 ≈ 1 (treated as 1 in most problems).
• Optically denser medium: higher n (e.g., glass n ≈ 1.5, diamond n = 2.42).
• Optically rarer medium: lower n (e.g., air n ≈ 1).
• When light goes from rarer to denser medium (e.g., air to glass): it bends toward the normal (θ₂ < θ₁).
• When light goes from denser to rarer medium (e.g., glass to air): it bends away from the normal (θ₂ > θ₁).
| Medium | Refractive Index (n) | Speed of Light | Optical Density |
|---|---|---|---|
| Vacuum | 1.0000 | 3.00 × 10&sup8; m/s | Reference |
| Air | 1.0003 ≈ 1 | 2.999 × 10&sup8; m/s | Very low |
| Water (liquid) | 1.33 | 2.26 × 10&sup8; m/s | Low |
| Crown Glass | 1.52 | 1.97 × 10&sup8; m/s | Medium |
| Flint Glass | 1.70 | 1.76 × 10&sup8; m/s | High |
| Diamond | 2.42 | 1.24 × 10&sup8; m/s | Very high |
| Ice | 1.31 | 2.29 × 10&sup8; m/s | Low |
n₁ = absolute RI of medium 1 | n₂ = absolute RI of medium 2
v₁ = speed in medium 1 | v₂ = speed in medium 2
Reversibility: n₁₂ = 1/n₂₁ (RI from medium 2 to medium 1 = reciprocal of RI from 1 to 2)
3. Refraction Through a Glass Slab — Lateral Displacement
💡 Ray Diagram: Refraction Through a Rectangular Glass Slab
• The incident ray and the emergent ray are parallel to each other (same angle, same direction), but laterally displaced.
• The emergent ray is shifted sideways from the original direction — this sideways shift is called lateral displacement (d).
• Lateral displacement: d = t sin(i−r)/cos(r), where t = thickness of slab, i = angle of incidence, r = angle of refraction.
• Lateral displacement increases with: (1) increasing angle of incidence, (2) increasing slab thickness, (3) increasing refractive index of glass.
• When i = 0 (normal incidence): no bending, no lateral displacement (ray passes straight through).
4. Real and Apparent Depth
Formula: n (of denser medium, viewed from rarer) = Real Depth / Apparent Depth
⇒ Apparent Depth = Real Depth / n
⇒ Shift (apparent rise) = Real Depth − Apparent Depth = Real Depth × (1 − 1/n)
Examples:
• A swimming pool 2 m deep appears (2/1.33) ≈ 1.5 m deep when viewed from above.
• A coin at the bottom of a water-filled vessel appears closer to the surface.
• A fish swimming 3 m below the water surface appears to be at 3/1.33 ≈ 2.25 m depth.
• Stars appear higher in the sky than their actual position (atmospheric refraction: apparent shift upward at horizon ≈ 0.5°, roughly equal to the Moon’s angular diameter).
5. Total Internal Reflection (TIR) and Critical Angle
⚡ Total Internal Reflection (TIR)
(1) Light must travel from a denser medium to a rarer medium (e.g., glass to air, water to air).
(2) The angle of incidence must be greater than the critical angle (i > C).
Critical Angle (C): The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is exactly 90° (refracted ray grazes the surface). When i > C, no refraction occurs — all light is reflected back into the denser medium (Total Internal Reflection).
Derivation of critical angle: At critical angle C, θ₂ = 90° (refracted ray along surface).
Using Snell’s law: n sin C = 1 × sin 90° = 1 ⇒ sin C = 1/n ⇒ C = sin²(1/n)
Critical angles for common materials:
• Water (n=1.33): C = sin²(1/1.33) = 48.8°
• Crown Glass (n=1.52): C = sin²(1/1.52) = 41.1°
• Diamond (n=2.42): C = sin²(1/2.42) = 24.4° — very small C means light bounces internally many times → extraordinary sparkle!
What happens at different angles (denser to rarer):
• i < C: Refraction occurs (some reflection, mostly refraction).
• i = C: Refracted ray grazes the surface (θ₂ = 90°).
• i > C: Total Internal Reflection (no refraction; all light reflects back inside denser medium).
6. Applications of Total Internal Reflection
7. Real-Life Examples of Refraction
8. Solved Numerical Problems
1 × sin 45° = 1.5 × sinθ₂
sinθ₂ = sin 45° / 1.5 = 0.7071 / 1.5 = 0.4714
θ₂ = sin²(0.4714)
C = sin²(0.6579)
1.33 × sin30° = 1.5 × sinθ₂
1.33 × 0.5 = 1.5 × sinθ₂
sinθ₂ = 0.665 / 1.5 = 0.4433
θ₂ = sin²(0.4433)
🌎 Complete AJKANT Optics Cluster — 4 Guides
9. Frequently Asked Questions (FAQ)
First Law: The incident ray, the refracted ray, and the normal to the refracting surface at the point of incidence all lie in the same plane.
Second Law (Snell’s Law): For a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given wavelength of light.
sinθ₁/sinθ₂ = n₂₁ = constant (called relative refractive index of medium 2 w.r.t. medium 1)
Equivalently: n₁ sinθ₁ = n₂ sinθ₂ (using absolute refractive indices)
Refractive index (n) of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium: n = c/v.
Factors affecting refractive index:
(1) Nature of the medium: Denser materials (more atoms/molecules per unit volume) have higher n (e.g., glass n=1.5, diamond n=2.42).
(2) Wavelength (colour) of light: n is different for different wavelengths. Violet light has higher n than red light in glass (this causes dispersion — prism separates white light into spectrum). This is called dispersion.
(3) Temperature: As temperature increases, density decreases, so n decreases slightly.
(4) Pressure: For gases, higher pressure increases density and hence n.
Note: Refractive index does NOT depend on the angle of incidence (Snell’s law shows n is constant for given media and wavelength).
Total Internal Reflection (TIR): When a light ray travels from a denser medium to a rarer medium and the angle of incidence exceeds the critical angle, no refraction occurs. All the light is completely reflected back into the denser medium. This phenomenon is called total internal reflection.
Conditions for TIR:
(1) Light must travel from denser to rarer medium (e.g., glass to air, water to air, glass to water if nᵊᵋᵃᴸᴸ > nᵏᵃᵗᵃᵅ).
(2) Angle of incidence must be greater than the critical angle: i > C, where sin C = nᵅᵃᵅᵃᵅ/nₒᵃᵗᴸᵃᵅ = 1/n (when rarer medium is air).
Critical Angle: The specific angle of incidence for which the angle of refraction is exactly 90° (refracted ray grazes the boundary surface). sin C = 1/n for glass-air interface.
For crown glass (n=1.52): C = 41.1°
For diamond (n=2.42): C = 24.4° (very small — explains brilliant sparkle!)
Optical fibre is a thin, flexible strand of very pure glass or plastic (diameter ≈ 10 μm for single-mode, 50–100 μm for multi-mode) used to transmit light signals over long distances with minimal loss.
Structure:
• Core: Central glass strand with high refractive index (nₑᵓᵅᵃ ≈ 1.48).
• Cladding: Outer glass layer with lower refractive index (nₒᵈᵃₒₒᵄᵗᵊ ≈ 1.46).
• Buffer coating: Protective plastic outer layer.
Working principle: Light enters the core at one end. At every core-cladding interface, the angle of incidence (measured from the normal to the curved surface) exceeds the critical angle C. Therefore, TIR occurs at each bounce, and the light zigzags through the core from one end to the other with virtually no loss — even through bends and curves.
Applications: (1) High-speed internet (broadband fibre cables). (2) International submarine cables carrying internet traffic between continents. (3) Medical endoscopes (imaging inside body). (4) Industrial inspection cameras. (5) Decorative optical fibre lamps.
When an observer in air looks at an object submerged in water, light rays from the object refract at the water-air boundary, bending away from the normal (going from denser water to rarer air). The observer’s eye receives the diverging refracted rays and, extending them backward in straight lines (the eye/brain does not account for refraction), appears to see the object at a point closer to the surface than its actual position.
Formula:
n (of water) = Real Depth / Apparent Depth
⇒ Apparent Depth = Real Depth / n
For water (n = 1.33): A pool 2 m deep appears only 2/1.33 = 1.5 m deep.
Apparent shift (how much closer it appears):
Shift = Real Depth − Apparent Depth = d(1 − 1/n)
For 2 m pool: Shift = 2(1 − 1/1.33) = 2 × 0.25 = 0.5 m (appears 0.5 m closer than it is).
Caution in swimming pools: This is why pools always appear shallower than they are — a potentially dangerous illusion for non-swimmers who underestimate the depth.
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