What you'll learn
This topic covers the behaviour of light as it travels through different media, reflects off surfaces, and refracts when crossing boundaries between materials. Understanding reflection, refraction, total internal reflection, dispersion, and how lenses form images is essential for Paper 2 (Core) and Paper 4 (Extended) where questions on ray diagrams, critical angle calculations, and the electromagnetic spectrum regularly appear.
Key terms and definitions
Reflection — the bouncing of light off a surface where the angle of incidence equals the angle of reflection, both measured from the normal.
Refraction — the change in direction of light as it passes from one medium to another due to a change in speed, bending towards the normal when entering a denser medium.
Normal — an imaginary line perpendicular to the surface at the point where the light ray strikes.
Critical angle — the angle of incidence in the denser medium that produces an angle of refraction of 90° in the less dense medium.
Total internal reflection — when light travelling from a denser to a less dense medium strikes the boundary at an angle greater than the critical angle, all light reflects back into the denser medium.
Refractive index — the ratio of the speed of light in a vacuum to the speed of light in a medium, represented by n.
Dispersion — the separation of white light into its component colours due to different wavelengths refracting by different amounts.
Focal length — the distance from the centre of a lens to its principal focus where parallel rays converge (converging lens) or appear to diverge from (diverging lens).
Core concepts
Reflection of light
Light reflects off surfaces following the law of reflection: the angle of incidence equals the angle of reflection (i = r), with both angles measured from the normal to the surface.
Specular reflection occurs on smooth surfaces like mirrors where parallel incident rays produce parallel reflected rays, creating clear images. Diffuse reflection occurs on rough surfaces where parallel incident rays scatter in many directions, preventing image formation but allowing the surface to be seen from any angle.
Mirror ray diagrams require:
- Drawing incident rays to the mirror surface
- Constructing the normal (perpendicular to the surface)
- Ensuring the reflected ray makes an equal angle on the opposite side of the normal
- Using a ruler for straight lines and marking angles clearly
Plane mirrors produce virtual images that are:
- The same size as the object
- The same distance behind the mirror as the object is in front
- Laterally inverted (left and right swapped)
- Upright
Refraction of light
When light crosses a boundary between two transparent media, it changes speed and direction (unless entering perpendicular to the boundary). Light slows down entering a denser medium and speeds up entering a less dense medium.
Key refraction principles:
- Light bends towards the normal when entering a denser medium (e.g., air to glass)
- Light bends away from the normal when entering a less dense medium (e.g., glass to air)
- Light entering perpendicular to the boundary (along the normal) does not change direction but still changes speed
- The frequency of light remains constant; wavelength changes with speed
The refractive index (n) quantifies how much a medium slows light:
n = speed of light in vacuum / speed of light in medium
For air, n ≈ 1.0; for water, n ≈ 1.33; for glass, n ≈ 1.5
Snell's Law relates angles and refractive indices at a boundary:
n₁ sin θ₁ = n₂ sin θ₂
where θ₁ is the angle of incidence in medium 1 and θ₂ is the angle of refraction in medium 2.
Real-world refraction effects:
- Swimming pools appear shallower than actual depth
- Objects underwater appear closer than they are
- Mirages in deserts caused by hot air layers having different refractive indices
- Atmospheric refraction makes the sun visible even after it has geometrically set
Total internal reflection and critical angle
Total internal reflection only occurs when:
- Light travels from a more dense to a less dense medium (e.g., glass to air)
- The angle of incidence exceeds the critical angle
At the critical angle (c), the refracted ray travels along the boundary (angle of refraction = 90°). For angles greater than c, no refraction occurs—all light reflects internally.
Calculating critical angle using refractive indices:
sin c = n₂ / n₁
For a glass-air boundary where nglass = 1.5 and nair = 1.0:
sin c = 1.0 / 1.5 = 0.667
c = 42°
Applications of total internal reflection:
Optical fibres — thin glass or plastic fibres transmit light signals over long distances. Light enters one end at an angle exceeding the critical angle and reflects repeatedly off the internal surface without escaping. Used in:
- Telecommunications (internet and telephone signals)
- Medical endoscopes for internal body examination
- Decorative lighting
Prisms in periscopes and binoculars — 45° prisms reflect light through 90° or 180° more efficiently than mirrors, with no loss through absorption.
Dispersion and the visible spectrum
White light comprises a continuous spectrum of colours, each with different wavelengths. Dispersion separates these colours because different wavelengths refract by different amounts in a medium.
When white light enters a glass prism:
- Violet light (shortest wavelength, ~400 nm) slows most and refracts most
- Red light (longest wavelength, ~700 nm) slows least and refracts least
- The spectrum emerges in order: red, orange, yellow, green, blue, indigo, violet (ROYGBIV)
The refractive index varies slightly with wavelength—this is called dispersion. Violet light has a higher refractive index than red light in the same medium.
Rainbows form through dispersion when sunlight refracts entering water droplets, reflects internally, then refracts again leaving the droplet, separating into colours.
Converging and diverging lenses
Converging (convex) lenses are thicker in the middle and bring parallel light rays to a focus at the principal focus (F). The distance from the lens centre to F is the focal length (f).
Ray diagram rules for converging lenses (drawing the image):
- A ray parallel to the principal axis refracts through the principal focus
- A ray through the optical centre continues straight without deviation
- A ray through the principal focus on the object side refracts parallel to the principal axis
The image characteristics depend on object distance:
- Object beyond 2f: real, inverted, diminished image between f and 2f (used in cameras)
- Object at 2f: real, inverted, same size image at 2f
- Object between f and 2f: real, inverted, magnified image beyond 2f (used in projectors)
- Object at f: no image forms (rays emerge parallel)
- Object inside f: virtual, upright, magnified image on same side as object (used in magnifying glasses)
Diverging (concave) lenses are thinner in the middle and spread parallel light rays so they appear to come from the principal focus.
Diverging lenses always produce:
- Virtual images
- Upright images
- Diminished images
- Images on the same side as the object
Applications:
- Spectacles for short-sighted (myopic) people
- Camera viewfinders
- Door peepholes
The lens equation relates object distance (u), image distance (v), and focal length (f):
1/f = 1/u + 1/v
Magnification = image height / object height = image distance / object distance
The electromagnetic spectrum
Light is one part of the electromagnetic spectrum—a family of waves that all:
- Transfer energy
- Travel at the same speed in a vacuum (3.0 × 10⁸ m/s)
- Are transverse waves (oscillations perpendicular to energy transfer direction)
- Can travel through a vacuum
- Can be reflected, refracted, and diffracted
The complete spectrum in order of increasing wavelength (decreasing frequency and energy):
Gamma rays (< 0.01 nm)
- Produced by radioactive decay and nuclear reactions
- Medical uses: sterilising equipment, cancer treatment
- Dangers: kills living cells, causes cancer and mutations
X-rays (0.01–10 nm)
- Produced by high-energy electron bombardment of metal targets
- Medical uses: imaging bones and teeth, airport security scanners
- Dangers: ionising radiation damages cells, causes cancer with repeated exposure
Ultraviolet (UV) (10–400 nm)
- Emitted by very hot objects and the Sun
- Uses: security markings, fluorescent lamps, sterilising water, vitamin D production in skin
- Dangers: skin cancer, sunburn, eye damage (cataracts)
Visible light (400–700 nm)
- The only part humans can detect with eyes
- Used for vision, photography, optical fibres, lasers
- Different colours have different wavelengths (violet shortest, red longest)
Infrared (IR) (700 nm–1 mm)
- Emitted by all warm objects
- Uses: remote controls, thermal imaging, cooking (grills and toasters), optical fibre communication, night-vision equipment
- Dangers: skin burns at high intensity
Microwaves (1 mm–30 cm)
- Uses: mobile phone communication, satellite TV transmission, microwave ovens (2.45 GHz frequency absorbed by water molecules)
- Dangers: internal heating of body tissue
Radio waves (> 30 cm, up to km)
- Longest wavelength, lowest frequency
- Uses: television broadcasting, radio broadcasting, Bluetooth, WiFi
- Different wavelengths for different purposes (long wave, medium wave, short wave, VHF, UHF)
- Generally safe at normal exposure levels
All electromagnetic waves follow: speed (c) = frequency (f) × wavelength (λ)
Worked examples
Example 1: Critical angle calculation
A ray of light travels from diamond (n = 2.42) into air (n = 1.00). Calculate the critical angle for the diamond-air boundary.
Solution:
Using sin c = n₂ / n₁
sin c = 1.00 / 2.42 = 0.413
c = sin⁻¹(0.413) = 24.4°
The critical angle is 24.4° [2 marks: 1 for correct formula, 1 for correct calculation]
Example 2: Lens calculation
A converging lens has a focal length of 15 cm. An object is placed 30 cm from the lens. Calculate:
(a) The image distance
(b) The magnification
Solution:
(a) Using 1/f = 1/u + 1/v
1/15 = 1/30 + 1/v
1/v = 1/15 − 1/30 = 2/30 − 1/30 = 1/30
v = 30 cm [2 marks]
(b) Magnification = v / u = 30 / 30 = 1.0
The image is the same size as the object. [1 mark]
Example 3: Electromagnetic spectrum properties
The table shows three types of electromagnetic radiation.
| Type | Wavelength |
|---|---|
| A | 550 nm |
| B | 5 cm |
| C | 0.01 nm |
(a) Identify each type of radiation.
(b) Which has the highest frequency?
(c) State one use for radiation type B.
Solution:
(a) A = visible light (green); B = microwaves; C = X-rays [3 marks]
(b) Type C (X-rays) — shortest wavelength means highest frequency [1 mark]
(c) Satellite communication / microwave ovens / mobile phones [1 mark for any correct use]
Common mistakes and how to avoid them
Measuring angles from the surface instead of the normal — angles of incidence, reflection, and refraction are always measured from the normal (perpendicular line), not from the boundary surface itself. Draw the normal first and use a protractor correctly.
Confusing real and virtual images — real images form where light rays actually converge and can be projected onto a screen; virtual images form where light rays appear to come from and cannot be projected. Virtual images are always on the same side of the lens as the object.
Applying total internal reflection in wrong direction — total internal reflection only occurs when light travels from a denser medium to a less dense medium (e.g., glass to air, not air to glass). Check the direction of travel carefully.
Drawing refracted rays bending the wrong way — when light enters a denser medium it bends towards the normal; when entering a less dense medium it bends away from the normal. The ray should be closer to the normal in the medium with higher refractive index.
Mixing up the electromagnetic spectrum order — memorise the sequence using wavelength or frequency consistently. Radio waves have the longest wavelength (lowest frequency); gamma rays have the shortest wavelength (highest frequency).
Incorrect ray diagram technique — use a ruler for all straight lines, draw arrows to show light direction, mark the principal axis and focal points clearly, and extend rays with dashed lines where needed. Examiners deduct marks for poor diagram technique even if understanding is correct.
Exam technique for Light
Ray diagram questions (4-6 marks) — command words include "draw" or "complete the ray diagram." Draw at least two construction rays for lenses (three is safer), use a ruler, add arrows showing direction, and draw image formation clearly. Label the image position and state whether it is real or virtual.
Calculation questions using refractive index or lens equations — show working clearly in steps. For critical angle problems, ensure your calculator is in degree mode. For lens calculations, watch positive/negative sign conventions (real images have positive v, virtual images have negative v in some mark schemes).
"Explain" questions on total internal reflection or dispersion (3-4 marks) — structure answers with conditions first, then process, then outcome. For total internal reflection: state the two necessary conditions (denser to less dense medium, angle exceeds critical angle), describe what happens (all light reflects back), and give the consequence (no refraction occurs).
Electromagnetic spectrum questions — learn one use and one danger for each type. Questions often ask to identify wave type from wavelength, order types by frequency/wavelength, or describe applications. The phrase "all electromagnetic waves travel at the same speed in a vacuum" is worth remembering for comparison questions.
Quick revision summary
Reflection: angle of incidence equals angle of reflection, measured from the normal. Refraction: light bends towards the normal entering a denser medium, away when entering a less dense medium. Total internal reflection occurs when light in a denser medium exceeds the critical angle at a boundary. Dispersion separates white light into colours because different wavelengths refract differently. Converging lenses focus parallel rays; diverging lenses spread them. The electromagnetic spectrum ranges from radio waves (longest wavelength) to gamma rays (shortest wavelength), all travelling at 3.0 × 10⁸ m/s in a vacuum.