Refraction of Light – ICSE Class 10 Physics

        Refraction is one of the most fascinating chapters in ICSE Physics — it explains why a pencil looks bent in water, how lenses work, and even why diamonds sparkle! The board exam loves this chapter: expect at least one lens numerical (3-4 marks), a TIR question, and definitions of refractive index and power of lens. Let's break it all down properly.
    

1) Refraction of Light — What and Why?

Refraction is the bending of light when it passes from one transparent medium to another. This happens because the speed of light changes when it enters a different medium.

When light goes from a rarer to a denser medium (air → water), it bends towards the normal. Speed decreases.
When light goes from a denser to a rarer medium (water → air), it bends away from the normal. Speed increases.

Refraction occurs because the speed of light is different in different media. Speed of light in vacuum (c) = 3 × 10⁸ m/s (maximum possible)

2) Laws of Refraction

The incident ray, refracted ray, and the normal at the point of incidence all lie in the same plane.
The ratio of sin i to sin r is constant for a given pair of media. This is Snell's law.

Snell's law: sin i / sin r = constant = n₂₁ n₂₁ = refractive index of medium 2 with respect to medium 1

3) Refractive Index

Refractive index tells you how much a medium bends light — or more precisely, how much it slows down light compared to vacuum.

Type	Formula	What it means
Absolute refractive index (n)	n = c / v	Speed of light in vacuum / speed of light in the medium
Relative refractive index (n₂₁)	n₂₁ = v₁ / v₂ = n₂ / n₁	Ratio of speeds in medium 1 and medium 2

Common Refractive Indices to Remember

Medium	Refractive Index
Air (vacuum)	1.00 (by definition)
Water	1.33
Glass	1.5 (approximately)
Diamond	2.42

The higher the refractive index, the more optically dense the medium is. Light bends more when entering a medium with higher n. That's why diamonds sparkle so much — n = 2.42 is very high.

Refractive index depends on: (1) Nature of the medium, (2) Wavelength/colour of light (violet bends more than red), (3) Temperature. ICSE loves asking these factors — it's a common 2-marker.

4) Refraction Through a Glass Slab — Lateral Shift

When light passes through a rectangular glass slab, the emergent ray is parallel to the incident ray but shifted sideways. This sideways shift is called lateral shift.

Lateral shift (T) = t × sin(i - r) / cos r t = thickness of the glass slab

Factors Affecting Lateral Shift

Thickness of the slab (t) — thicker slab → more shift
Angle of incidence (i) — larger i → more shift (up to a point)
Refractive index of the glass — higher n → more bending → more shift
Wavelength of light — violet shifts more than red

For a glass slab: the emergent ray is always parallel to the incident ray. This is a VERY common diagram question — draw the slab, show incident ray bending towards normal on entry, away from normal on exit, and label the lateral shift. Easy 3 marks.

5) Lenses — Convex and Concave

Property	Convex Lens	Concave Lens
Shape	Thick in the middle, thin at edges	Thin in the middle, thick at edges
Nature	Converges light (converging lens)	Diverges light (diverging lens)
Focal length sign	Positive (+f)	Negative (-f)
Image types	Real + Virtual (both possible)	Always virtual, erect, diminished
Uses	Magnifying glass, camera, projector, eyeglasses for hypermetropia	Eyeglasses for myopia (shortsightedness), peepholes

6) Lens Formula and Sign Convention

The lens formula is the most important tool for solving numericals. ICSE uses the Cartesian sign convention:

Object distance (u) is always negative (object on left side of lens)
Focal length (f) is positive for convex, negative for concave
Image distance (v) is positive if image is on right (real), negative if on left (virtual)
Height above principal axis = positive, below = negative

Lens formula: 1/f = 1/v - 1/u Magnification: m = h' / h = v / u

7) Power of a Lens

Power of a lens tells you how strongly it converges or diverges light. More power = more bending.

P = 1 / f (where f is in metres) SI unit: dioptre (D) Convex lens: P is positive (+) Concave lens: P is negative (-)

Combination of Lenses (Lenses in Contact)

When two lenses are placed in contact, the combined power is:

P = P₁ + P₂ 1/F = 1/f₁ + 1/f₂

This is why eye doctors combine lenses: the total power is just the sum. If a convex lens of +2D and a concave lens of -1D are combined, the net power is +1D (converging).

8) Image Formation by Convex Lens (6 Cases)

Object Position	Image Position	Nature	Size
At infinity	At F₂	Real, inverted	Highly diminished (point)
Beyond 2F₁	Between F₂ and 2F₂	Real, inverted	Diminished
At 2F₁	At 2F₂	Real, inverted	Same size
Between F₁ and 2F₁	Beyond 2F₂	Real, inverted	Enlarged
At F₁	At infinity	Real, inverted	Highly enlarged
Between O and F₁	Same side as object	Virtual, erect	Enlarged

9) Image Formation by Concave Lens (2 Cases)

Object Position	Image Position	Nature	Size
At infinity	At F₁ (on object side)	Virtual, erect	Highly diminished
At finite distance	Between O and F₁	Virtual, erect	Diminished

10) Total Internal Reflection (TIR)

Total internal reflection is the complete reflection of light back into the denser medium when it strikes the boundary at an angle greater than the critical angle.

Conditions for TIR

Light must travel from a denser medium to a rarer medium.
The angle of incidence must be greater than the critical angle (i > C).

Critical Angle

sin C = n₂ / n₁ Where n₁ > n₂ (denser to rarer)

For a glass-air boundary (n_glass = 1.5, n_air = 1): sin C = 1/1.5 = 0.667, so C ≈ 42°. For water-air (n = 1.33): C ≈ 49°.

Real-Life Applications of TIR (ICSE Loves These!)

Application	How TIR is Used
Optical fibres	Light signals are transmitted through thin glass fibres by repeated TIR. Used in telecommunications, endoscopy, internet cables.
Mirage (looming)	On hot days, air near ground is hotter (rarer). Light from sky bends away from normal → TIR occurs → you see a false reflection of the sky looking like water.
Sparkling diamond	Diamond has a very high n (2.42), so critical angle is very low (~24°). Light entering undergoes multiple TIRs before exiting, giving that brilliant sparkle.
Totally reflecting prisms	Used in periscopes and binoculars instead of mirrors. A right-angled prism can deviate light by 90° or 180° with 100% reflection.

11) Prism — Deviation and Dispersion

A prism is a transparent medium bounded by two plane surfaces inclined at an angle of prism (A). Light passing through a prism deviates from its original path.

Angle of deviation: δ = i + e - A At minimum deviation: i = e and δ = δ_m Refractive index of prism: n = sin((A + δ_m) / 2) / sin(A / 2)

Dispersion of White Light

When white light passes through a prism, it splits into its constituent colours — VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red). This is called dispersion.

Violet deviates the most (shortest wavelength, bends most)
Red deviates the least (longest wavelength, bends least)
Dispersion happens because different colours have different wavelengths and the refractive index of the medium is different for different wavelengths

12) Solved Numericals

Numerical 1 — Refractive Index

Speed of light in vacuum is 3 × 10⁸ m/s and in glass is 2 × 10⁸ m/s. Find the refractive index of glass.

n = c / v = (3 × 10⁸) / (2 × 10⁸) = 1.5

Numerical 2 — Snell's Law

Light enters water (n = 1.33) from air at an angle of incidence of 45°. Find the angle of refraction.

n = sin i / sin r → sin r = sin i / n sin 45° = 0.707 sin r = 0.707 / 1.33 = 0.531 r = sin⁻¹(0.531) ≈ 32.1°

Numerical 3 — Lens Formula

An object is placed at 30 cm from a convex lens of focal length 15 cm. Find the image distance and magnification.

Given: u = -30 cm, f = +15 cm 1/f = 1/v - 1/u 1/15 = 1/v - 1/(-30) 1/15 = 1/v + 1/30 1/v = 1/15 - 1/30 = (2 - 1)/30 = 1/30 v = +30 cm (image on right side, real) m = v/u = 30/(-30) = -1 (same size, inverted)

Numerical 4 — Power of Lens

A convex lens has a focal length of 25 cm. Find its power.

f = 25 cm = 0.25 m P = 1 / f = 1 / 0.25 = +4 D

Numerical 5 — Combination of Lenses

A convex lens of power +3 D and a concave lens of power -2 D are placed in contact. Find the combined power and focal length.

P = P₁ + P₂ = 3 + (-2) = +1 D f = 1 / P = 1 / 1 = 1 m = 100 cm

Numerical 6 — Critical Angle

The refractive index of diamond is 2.42. Find its critical angle with respect to air.

sin C = 1 / n = 1 / 2.42 = 0.413 C = sin⁻¹(0.413) ≈ 24.4°

13) Quick Revision — Night Before the Exam

Refraction: bending of light due to speed change. Denser → bends towards normal
Snell's law: sin i / sin r = n (constant for a pair of media)
Refractive index: n = c/v. Higher n = optically denser = more bending
Lateral shift: emergent ray is parallel to incident ray but shifted sideways
Lens formula: 1/f = 1/v - 1/u. u is always negative
Magnification: m = v/u = h'/h. Negative = real/inverted, positive = virtual/erect
Power of lens: P = 1/f (in metres). Unit = dioptre (D). Convex = +, Concave = -
Combined power: P = P₁ + P₂
TIR conditions: denser → rarer AND i > C
sin C = n₂/n₁ — critical angle formula
Applications of TIR: optical fibres, mirage, diamond sparkle, totally reflecting prisms
Dispersion: white light splits into VIBGYOR. Violet deviates most, red least
Prism formula: δ = i + e - A. At minimum deviation: i = e

Common Mistakes That Cost Marks

❌ Forgetting the sign convention — u is ALWAYS negative in ICSE Cartesian system
❌ Using the mirror formula (1/f = 1/v + 1/u) for lenses — lens formula is 1/f = 1/v - 1/u
❌ Not converting cm to m for power of lens (P = 1/f where f must be in metres)
❌ Confusing convex and concave — convex = converging (+f), concave = diverging (-f)
❌ Writing "dispersion" when asked "refraction" — they're different!
❌ Saying TIR occurs when light goes from rarer to denser — it's the OPPOSITE (denser to rarer)
❌ Forgetting units: refractive index has NO unit (it's a ratio), Power = dioptre (D)

        Final tip: Refraction is a chapter where diagrams earn you marks. Practice drawing ray diagrams for convex lens (all 6 cases), glass slab lateral shift, prism dispersion, and TIR. In the exam, draw neatly with a pencil and label every ray, angle, and point. Also practice at least 5-6 lens formula numericals before the exam — once you get the sign convention right, they're all the same pattern. You've got this! 🔍
    

14) All Formulas at One Glance

Refractive index (absolute): n = c / v Relative refractive index: n₂₁ = v₁ / v₂ = n₂ / n₁ Snell's law: n = sin i / sin r Lateral shift: T = t × sin(i - r) / cos r Lens formula: 1/f = 1/v - 1/u Magnification: m = v / u = h' / h Power of lens: P = 1 / f (metres) — unit: dioptre (D) Combined power: P = P₁ + P₂ Critical angle: sin C = n₂ / n₁ Prism deviation: δ = i + e - A Prism refractive index: n = sin((A + δ_m)/2) / sin(A/2)