Waves and Light

What you'll learn

This section covers the fundamental properties of waves, the electromagnetic spectrum, and the behaviour of light. You will encounter questions on wave properties, reflection, refraction, total internal reflection, and the electromagnetic spectrum in Paper 01 (multiple choice), Paper 02 (structured questions), and the alternative to School-Based Assessment. Understanding these concepts is essential for scoring well in Section B of most CSEC Physics papers.

Key terms and definitions

Wavelength (λ) — the distance between two consecutive points in phase on a wave, measured in metres (m).

Frequency (f) — the number of complete waves passing a point per second, measured in hertz (Hz).

Amplitude — the maximum displacement of a wave from its rest position, measured in metres (m) or appropriate units.

Transverse wave — a wave in which particles vibrate perpendicular to the direction of energy transfer; examples include light waves and water waves.

Longitudinal wave — a wave in which particles vibrate parallel to the direction of energy transfer; sound waves are longitudinal.

Refraction — the change in direction of a wave when it passes from one medium to another due to a change in speed.

Total internal reflection — the complete reflection of a light ray inside a material at the boundary with a less dense medium, occurring when the angle of incidence exceeds the critical angle.

Electromagnetic radiation — energy transmitted as waves that do not require a medium for propagation, traveling at 3.0 × 10⁸ m/s in a vacuum.

Core concepts

Wave properties and the wave equation

All waves transfer energy without transferring matter. The fundamental relationship connecting wave properties is:

Wave speed (v) = frequency (f) × wavelength (λ)

v = fλ

Where:

• v is measured in metres per second (m/s)
• f is measured in hertz (Hz)
• λ is measured in metres (m)

This equation applies to all wave types and appears frequently in CSEC calculations. The period (T) of a wave is the time taken for one complete wave to pass a point, related to frequency by T = 1/f.

Key characteristics of waves:

• Waves can be reflected (bounced back from a surface)
• Waves can be refracted (change direction when entering a new medium)
• Waves can be diffracted (spread out when passing through gaps or around obstacles)
• Waves can interfere (superpose when they meet)
• Waves transport energy and information, not matter

Transverse and longitudinal waves

Transverse waves have vibrations perpendicular to the direction of energy transfer. Examples include:

• All electromagnetic waves (light, radio waves, X-rays)
• Water waves (ripples on the Caribbean Sea)
• Waves on strings or ropes

Longitudinal waves have vibrations parallel to the direction of energy transfer. The primary example is sound waves, which consist of compressions (regions of high pressure) and rarefactions (regions of low pressure). Sound requires a medium and cannot travel through a vacuum.

The electromagnetic spectrum

The electromagnetic spectrum consists of seven main regions arranged in order of increasing wavelength (decreasing frequency and energy):

1. Gamma rays — shortest wavelength (10⁻¹² m), highest frequency; produced by radioactive decay; used in cancer treatment and sterilizing medical equipment
2. X-rays — wavelength around 10⁻¹⁰ m; used in medical imaging to detect broken bones; absorbed by dense materials like bone and metal
3. Ultraviolet (UV) — wavelength around 10⁻⁸ m; causes tanning and skin damage; high intensity UV radiation in the Caribbean requires sun protection
4. Visible light — wavelength 4 × 10⁻⁷ m (violet) to 7 × 10⁻⁷ m (red); detected by human eyes; enables photosynthesis in plants like sugar cane and cocoa
5. Infrared (IR) — wavelength around 10⁻⁵ m; felt as heat; used in remote controls and thermal imaging cameras
6. Microwaves — wavelength around 10⁻² m; used in microwave ovens and satellite communications across the Caribbean region
7. Radio waves — longest wavelength (up to 10⁴ m), lowest frequency; used for radio and television broadcasting throughout Trinidad, Jamaica, and other Caribbean territories

All electromagnetic waves travel at 3.0 × 10⁸ m/s (the speed of light) in a vacuum. They differ only in wavelength and frequency. The relationship v = fλ applies, so higher frequency waves have shorter wavelengths.

Reflection of light

Reflection occurs when light bounces off a surface. The law of reflection states:

Angle of incidence = Angle of reflection

Both angles are measured from the normal — an imaginary line perpendicular to the reflecting surface at the point of incidence.

Types of reflection:

• Regular reflection (specular reflection) — occurs on smooth surfaces like mirrors; parallel incident rays produce parallel reflected rays, forming clear images
• Diffuse reflection — occurs on rough surfaces like paper or concrete blocks used in Caribbean construction; parallel incident rays scatter in many directions, preventing clear image formation

Properties of plane mirror images:

• Image is the same size as the object
• Image is the same distance behind the mirror as the object is in front
• Image is virtual (cannot be projected onto a screen)
• Image is laterally inverted (left and right are reversed)
• A line joining the object to its image is perpendicular to the mirror

Refraction of light

Refraction occurs because light travels at different speeds in different media. Light travels fastest in a vacuum (3.0 × 10⁸ m/s) and slows down in transparent materials.

Refraction rules:

• Light entering a denser medium (air → glass or air → water) slows down and bends toward the normal
• Light entering a less dense medium (glass → air or water → air) speeds up and bends away from the normal
• Light striking a boundary at 90° (along the normal) continues straight through without bending, though its speed still changes

Refractive index (n) measures how much a material slows light:

n = speed of light in vacuum / speed of light in material

For most transparent materials:

• Water: n ≈ 1.33
• Glass: n ≈ 1.5
• Diamond: n ≈ 2.4

Higher refractive index means light bends more. This explains why objects underwater in Tobago's coral reefs appear closer than they actually are, and why a straw in a glass of mauby appears bent at the surface.

Snell's Law relates angles and refractive indices:

n₁ sin θ₁ = n₂ sin θ₂

Where θ₁ is the angle of incidence, θ₂ is the angle of refraction, and n₁ and n₂ are the refractive indices of the two media.

Total internal reflection and critical angle

Total internal reflection occurs when light travels from a dense medium toward a less dense medium (e.g., glass to air or water to air) and the angle of incidence exceeds a specific value.

The critical angle (c) is the angle of incidence in the denser medium that produces an angle of refraction of 90°. For angles greater than the critical angle, all light is reflected back into the denser medium — no refraction occurs.

For a medium with refractive index n (relative to air):

sin c = 1/n

Applications of total internal reflection:

• Optical fibers — used in telecommunications networks connecting Caribbean islands; light signals travel along glass fibers by repeated total internal reflection, carrying internet and telephone data
• Periscopes and prisms — used in optical instruments; 45° prisms reflect light through 90° or 180°
• Diamonds — high refractive index (2.4) gives a small critical angle (about 24°), causing multiple internal reflections that create sparkle

Conditions required:

1. Light must travel from a denser medium to a less dense medium
2. Angle of incidence must exceed the critical angle

Dispersion of light

Dispersion is the separation of white light into its component colors (spectrum) due to different wavelengths being refracted by different amounts. When white light passes through a triangular glass prism:

• Violet light (shortest wavelength) is refracted most
• Red light (longest wavelength) is refracted least
• The visible spectrum produced is: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV)

This occurs because the refractive index of glass varies slightly with wavelength. Rainbows form when sunlight is dispersed by water droplets in the atmosphere during Caribbean rainstorms — light is refracted entering the droplet, internally reflected at the back surface, then refracted again as it exits.

Worked examples

Example 1: Wave equation calculation

Question: Radio waves from a Jamaican FM station have a frequency of 94.5 MHz. Calculate the wavelength of these radio waves. (Speed of electromagnetic waves = 3.0 × 10⁸ m/s)

Solution:

Given:

• f = 94.5 MHz = 94.5 × 10⁶ Hz = 9.45 × 10⁷ Hz
• v = 3.0 × 10⁸ m/s

Using v = fλ

λ = v/f

λ = (3.0 × 10⁸ m/s) / (9.45 × 10⁷ Hz)

λ = 3.17 m

Answer: The wavelength is 3.2 m (to 2 significant figures)

Marks: This would typically earn 3 marks — 1 for correct formula, 1 for substitution with correct conversion, 1 for correct answer with unit.

Example 2: Refraction and critical angle

Question: A ray of light travels from glass (refractive index 1.5) into air. Calculate the critical angle for the glass-air boundary.

Solution:

Given:

• n_glass = 1.5
• n_air = 1.0

For critical angle: sin c = n₂/n₁

sin c = 1.0/1.5

sin c = 0.667

c = sin⁻¹(0.667)

c = 41.8°

Answer: The critical angle is 42° (to 2 significant figures)

Mark scheme: 3 marks — 1 for correct formula, 1 for correct substitution, 1 for correct calculation with degree symbol.

Example 3: Electromagnetic spectrum knowledge

Question: (a) Name the electromagnetic wave with wavelength approximately 10⁻¹⁰ m. (1 mark) (b) State one use of this type of radiation. (1 mark) (c) Explain why all electromagnetic waves travel at the same speed in a vacuum but at different speeds in glass. (2 marks)

Solution:

(a) X-rays ✓

(b) Medical imaging / detecting broken bones / airport security scanning (any one) ✓

(c) In a vacuum there is no medium to interact with the waves, so all electromagnetic waves travel at c = 3.0 × 10⁸ m/s ✓. In glass, the wave speed depends on how the electromagnetic field interacts with the material's atoms, which varies with wavelength/frequency, causing different speeds ✓.

Common mistakes and how to avoid them

Mistake: Confusing the angle of incidence with the angle to the surface rather than to the normal. Correction: Always measure angles from the normal (perpendicular line), not from the surface itself. Draw the normal clearly in your diagrams.

Mistake: Stating that waves transfer matter or particles from one place to another. Correction: Waves transfer energy and information only. The medium particles vibrate in place but do not travel with the wave. Use the example of a crowd wave in the stadium — people stand and sit but don't move along the row.

Mistake: Writing that light speeds up when entering a denser medium. Correction: Light always slows down when entering a denser medium (higher refractive index). This slowing causes it to bend toward the normal. Only when leaving a dense medium for a less dense one does light speed up.

Mistake: Claiming that total internal reflection can occur when light travels from air to glass. Correction: Total internal reflection requires light to travel from a denser medium to a less dense medium. It cannot occur when light enters a denser medium from a less dense one.

Mistake: Confusing frequency and wavelength — thinking longer wavelength means higher frequency. Correction: Frequency and wavelength are inversely related: f = v/λ. Longer wavelength always means lower frequency (for constant wave speed). Gamma rays have the shortest wavelength and highest frequency.

Mistake: Forgetting to convert units, especially MHz to Hz or km to m in calculations. Correction: Always convert to base SI units (Hz, m, s) before substituting into equations. Write the conversion step clearly: 95 MHz = 95 × 10⁶ Hz.

Exam technique for Waves and Light

Understand command words: "State" requires a brief answer without explanation (1 mark). "Explain" requires a reason using physics principles (2-3 marks). "Calculate" requires formula, substitution, and answer with unit (typically 3 marks). "Describe" requires a sequence of points or a detailed account (2-4 marks).

Draw clear ray diagrams: Use a ruler and sharp pencil for all lines. Always include: normal line (dashed), incident ray with arrow, reflected/refracted ray with arrow, clearly marked angles, and labels. Ray diagrams typically earn 2-4 marks and lose marks easily for missing elements.

Show full working in calculations: Write the formula first, then substitute values with units, then calculate. Even if your final answer is wrong, you earn method marks for correct formula and substitution. For a 3-mark calculation, you can still earn 2 marks with one arithmetic error if your method is correct.

Learn the electromagnetic spectrum order: Questions frequently ask you to identify a wave type from its wavelength or to arrange waves in order. Create a memory aid using the first letters: "Great X-rays UV Light In My Room" for Gamma, X-ray, UV, Light, Infrared, Microwave, Radio. Know at least one use for each type.

Quick revision summary

Wave speed equals frequency times wavelength (v = fλ). Transverse waves vibrate perpendicular to energy transfer direction; longitudinal waves vibrate parallel. The electromagnetic spectrum ranges from gamma rays (shortest wavelength) to radio waves (longest), all traveling at 3.0 × 10⁸ m/s in vacuum. Reflection: angle of incidence equals angle of reflection, measured from the normal. Refraction: light bends toward the normal entering denser media, away from normal entering less dense media. Total internal reflection occurs when light in a dense medium strikes the boundary at an angle exceeding the critical angle (sin c = 1/n). White light disperses into a spectrum because different wavelengths refract differently.