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IGCSE Physics 0625 · Chapter 8 notes · ~11 min read

Light & the EM spectrum

Mirrors, refraction, total internal reflection, lenses, colour — and all seven families of electromagnetic waves with uses, dangers and a mnemonic.

Plane mirrorsRefraction & critical angleOptical fibresDispersionConverging lensesSight correctionElectromagnetic spectrumDigital & analogue signals
RSby Riyaz Sir
mentorriyaz.in
No tag = Core (everyone)EXTENDED Extended onlyhighlight = comes up again and againTest yourself at the end

In 30 seconds

  • Reflection: angle of incidence = angle of reflection, both measured from the normal.
  • Refraction: light bends towards the normal when it slows down (air → glass). EXT n = sin i ÷ sin r and n = 1 ÷ sin c.
  • Total internal reflection happens inside a dense material when the angle is bigger than the critical angle.
  • A converging lens makes a real image if the object is beyond F, and a virtual, magnified image if the object is inside F. EXT
  • The EM spectrum, from long to short wavelength: radio, microwave, infrared, visible, ultraviolet, X-ray, gamma. All travel at 3.0 × 10⁸ m/s in a vacuum.

By the end you can

  • Draw and use the law of reflection for a plane mirror and describe the image.
  • Describe refraction, the critical angle and total internal reflection, and calculate n. EXT
  • Describe dispersion and the colours of the spectrum.
  • Draw ray diagrams for a converging lens and describe the image.
  • List the EM waves in order with uses and dangers.

1Reflection

Plane mirrors

Normal — a line drawn at 90° to the surface at the point where the ray hits.

normalincident rayreflected rayirangle of incidence i = angle of reflection rboth angles are measured from the NORMAL
The law of reflection: angle of incidence (i) = angle of reflection (r). Both angles are measured from the normal, never from the mirror surface.
objectimage(virtual)ddimage: same size, upright, same distance behind the mirrorrays only APPEAR to come from the image (dotted lines)
The image in a plane mirror: same size as the object, upright, the same distance behind the mirror as the object is in front, and virtual.
  • A virtual image cannot be shown on a screen, because the rays only seem to come from it (dotted lines). The image is also laterally inverted (left and right swapped).
Worked example

A ray hits a plane mirror making an angle of 30° with the mirror surface. Find the angle of incidence and the angle between the incident and reflected rays.

  1. The normal is at 90° to the surface, so i = 90° − 30° = 60°
  2. r = i = 60°
  3. angle between incident and reflected rays = 60° + 60° = 120°
Worked example

EXT A person stands 2.0 m in front of a plane mirror. How far is the person from their image?

  1. The image is 2.0 m behind the mirror
  2. distance from the person = 2.0 + 2.0 = 4.0 m
Common mistakeMeasuring the angle of incidence from the mirror instead of from the normal.

2Refraction

Refraction of light

Refraction — the change in direction of light when it passes from one transparent material to another, caused by a change in speed.

irAIRGLASSslower in glass:bends TOWARDSthe normalemerges parallelto the original rayincidentrayrefracted ray
Air to glass: light slows down and bends TOWARDS the normal. Glass to air: it speeds up and bends AWAY. Through a parallel-sided block the ray comes out parallel to the one that went in.
  • A ray going into a denser material (air → glass or water) slows down and bends towards the normal. A ray leaving bends away from it. A ray along the normal (90° to the surface) goes straight through without bending.
  • EXT The refractive index n of a material shows how much it slows light: n = (speed in vacuum) ÷ (speed in the material). Glass has n ≈ 1.5.
EXT n = sin isin r
i = angle in air, r = angle in the material (both from the normal)
Worked example

EXT A ray enters glass at i = 45° and refracts at r = 28°. Find n.

  1. n = sin i ÷ sin r = sin 45° ÷ sin 28°
  2. = 0.707 ÷ 0.469
  3. = 1.5

Critical angle and total internal reflection

i < crefracts out(bends away)i = crefracted rayalong the surfacei > ctotal internalreflectionc = critical angle: only light going from a denser to a less dense medium
As the angle inside glass increases, the refracted ray bends towards the surface. At the critical angle c it runs along the surface. Beyond c all the light is reflected.

Critical angle (c) — the angle of incidence inside a dense material for which the refracted ray travels along the boundary (an angle of refraction of 90°).

  • Total internal reflection happens only if (1) light travels from a denser to a less dense material and (2) the angle of incidence is greater than the critical angle.
  • Below c, some light refracts out and a little is reflected. This partial reflection is called internal reflection.
EXT n = 1sin c
or sin c = 1 ÷ n
Worked example

EXT Glass has n = 1.5. Find the critical angle.

  1. sin c = 1 ÷ n = 1 ÷ 1.5 = 0.667
  2. c = 42°
  • Uses: bicycle reflectors and prisms in binoculars and periscopes.

Optical fibresEXTENDED

cladding: lower refractive indexcore (glass): the light zig-zags by total internal reflectionused for: endoscopes · broadband & phone signals · very little energy lost
Light zig-zags along the glass core by total internal reflection. The outer cladding has a lower refractive index.
  • Used for broadband, cable TV and phone signals (infrared or light pulses carry the data) and endoscopes that look inside the body. Almost no energy is lost, so signals travel a long way.

3Colour

Dispersion

white lightredorangeyellowgreenblueindigovioletviolet slows most and bends most; red bends least(this is why white light splits into a spectrum)
White light is a mixture of colours. In glass violet slows most, so it bends most; red bends least. A prism splits white light into a spectrum.
  • Dispersion is the splitting of white light into its colours.
  • Order: red, orange, yellow, green, blue, indigo, violet. Red has the longest wavelength and lowest frequency; violet has the shortest wavelength and highest frequency.
  • EXT Monochromatic light has a single frequency, so it is only one colour.
Exam tipIn a vacuum all colours travel at the same speed. They are only separated because they travel at different speeds in glass.

4Lenses

Converging lens ray diagrams

Principal axis — the line through the centre of the lens at right angles to it.

Principal focus (F) — the point where rays parallel to the axis meet after a converging lens.

Focal length — the distance from the centre of the lens to F.

  • A converging (convex) lens bends parallel rays so that they meet at F. A diverging (concave) lens spreads them out.
  • Draw a ray diagram using two rays: (1) a ray parallel to the axis, which refracts through F; (2) a ray through the centre of the lens, which goes straight on. The image is where they cross.
FF2F2Fobjectimageobject beyond 2F → image between F and 2F:real, inverted, diminished
Object beyond 2F: the image is between F and 2F, real, inverted and smaller.
Object positionImage
beyond 2Fbetween F and 2F; real, inverted, smaller
at 2Fat 2F; real, inverted, same size
between F and 2Fbeyond 2F; real, inverted, bigger
inside Fvirtual, upright, magnified EXT
  • A real image can be projected onto a screen. A virtual image cannot.

Magnifying glass and sight correctionEXTENDED

FFobjectimageto the eyeobject INSIDE F → virtual, upright, magnified image(a magnifying glass)
An object inside F gives an upright, magnified, virtual image. The lens is used as a magnifying glass.
Sight problemCauseCorrected with
short sight: far objects blurredlight focuses in front of the retinadiverging lens
long sight: near objects blurredlight focuses behind the retinaconverging lens

5The electromagnetic spectrum

Seven families of waves

long wavelength · low frequencyshort wavelength · high frequencyRadiowavesTV,radiobroadbandMicrowavescookingsatellitephonesheatingof tissueInfraredremotecontrolsheatersskinburnsVisiblelightsightphoto-synthesisUltravioletsterilisesecuritymarkingskincancerX-raysmedicalimagingscannerscelldamageGammarayssterilisecancertherapycancermutationblack = uses · red = dangersall are transverse waves that travel at 3 × 10⁸ m/s in a vacuum
All EM waves are transverse and travel at 3.0 × 10⁸ m/s in a vacuum, about the same in air. They differ in wavelength and frequency.
Memory trickRaging Martians Invaded Venus Using X-ray Guns — Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma (long wavelength to short).
WaveUsesDanger of too much
radioTV, radio, Bluetooth EXT—
microwavescooking, satellite signals, mobile phones EXT, wifi EXTheating of body cells inside the body
infraredremote controls, heaters, thermal cameras, burglar alarmsskin burns
visibleseeing, photography, photosynthesisvery bright light damages the eye
ultravioletsterilising water, security marks, sun bedsskin cancer and eye damage
X-raysmedical images, airport securitydamage to cells, cancer
gamma rayssterilising food and instruments, treating cancerdamage to cells, cancer
  • Satellite communication uses microwaves, which pass through the atmosphere. Both low-orbit and geostationary satellites are used (see the space chapter).
Worked example

EXT Sunlight takes how long to reach the Earth? (distance 1.5 × 10¹¹ m, speed of light 3.0 × 10⁸ m/s)

  1. t = distance ÷ speed = 1.5 × 10¹¹ ÷ 3.0 × 10⁸
  2. = 500 s
  3. = 8.3 minutes

Digital and analogue signalsEXTENDED

  • An analogue signal varies continuously. A digital signal has only two values (on and off, or 1 and 0).
  • Sound, pictures and data can be sent as either. A digital signal can be cleaned up (regenerated) as it travels, so it keeps a high quality over long distances. It can also carry more information and works with computers.

6Test yourself

Test yourself — cover the answers first

Quick check

  1. State the law of reflection.
  2. Give two properties of the image in a plane mirror.
  3. Which colour of light bends the most in a prism?
  4. Name the EM waves used for (a) cooking, (b) sterilising food.
  5. Which EM waves have the highest frequency?
  6. What two conditions are needed for total internal reflection?

Exam-style

  1. EXT Light goes from air into glass with i = 40°. The refractive index of the glass is 1.5. Find the angle of refraction.
  2. EXT The refractive index of water is 1.33. Find the critical angle.
  3. Describe the image formed by a converging lens (f = 10 cm) when an object is 30 cm from the lens. [3]
  4. EXT Explain how an optical fibre carries a signal. [3]
  5. State two differences between light waves and sound waves. [2]
Show answers
  1. The angle of incidence equals the angle of reflection (both from the normal).
  2. virtual, upright, same size as the object, same distance behind the mirror
  3. violet
  4. (a) microwaves (b) gamma rays
  5. gamma rays
  6. Light goes from a denser to a less dense material, and the angle of incidence is greater than the critical angle.
  7. sin r = sin i ÷ n = sin 40° ÷ 1.5 = 0.6428 ÷ 1.5 = 0.4285
    r = 25°
  8. sin c = 1 ÷ 1.33 = 0.752
    c = 49°
  9. The object is beyond 2F (20 cm)
    so the image is between F and 2F
    it is real, inverted and smaller
  10. Light enters the glass core
    and hits the core–cladding boundary at an angle bigger than the critical angle
    so it is totally internally reflected again and again along the fibre
  11. Light is transverse, sound is longitudinal
    light can travel through a vacuum, sound cannot (or: light travels much faster)
Practise this chapter
Reflection & refractionThin lensesElectromagnetic spectrum
Next chapterElectricity & circuits →
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