FOCUS POINT
SECTION 3 Waves
3.2.4 Dispersion of light
3.2.4 Dispersion of light
a
angle of deviation b
▲ Figure 3.2.45
Dispersion
When sunlight (white light) falls on a triangular glass prism (Figure 3.2.46a), a band of colours called a spectrum is obtained (Figure 3.2.46b). The effect is termed dispersion. It arises because white light is a mixture of many colours; the prism separates the colours because the refractive index of glass is different for each colour (it is greatest for violet light).
The traditional colours of the visible spectrum in order of increasing wavelength are: violet, indigo, blue, green, yellow, orange and red. In order of increasing frequency, the sequence is reversed.
Red light has the longest wavelength in the optical spectrum and hence the lowest frequency and is refracted least by the prism. Violet light has the shortest wavelength and the highest frequency in the optical spectrum and is refracted most by the prism.
red orange yellow green blue indigo violet white screen
spectrum prism
sunlight
▲ Figure 3.2.46a Forming a spectrum with a prism
▲ Figure 3.2.46b White light shining through cut crystal can produce several spectra.
Test yourself
17 Figure 3.2.47 shows a ray of light OP striking a glass prism and then passing through it. Which of the rays A to D is the correct representation of the emerging ray?
O
P
A B
C
D
▲ Figure 3.2.47
18 Which diagram in Figure 3.2.48 shows the correct path of the ray through the prism?
A B
C D
▲ Figure 3.2.48
Revision checklist
After studying Topic 3.2 you should know and understand:
✓ the meaning of the terms normal, angle of incidence and angle of reflection
✓ how to construct, calculate and measure reflections from plane mirrors
✓ the meaning of the terms refraction, critical angle, internal reflection and total internal reflection
✓ the terms used to describe images formed in lenses
✓ how simple converging and diverging lenses are used to correct long and short sight
✓ how a prism is used to produce a spectrum from white light
✓ the terms spectrum, dispersion
After studying Topic 3.2 you should be able to:
✓ describe an experiment to show that the angle of incidence equals the angle of reflection and use the law of reflection to solve problems
✓ describe the formation of an optical image in a plane mirror and recall the properties of the image
✓ describe an experiment to study refraction of light through transparent blocks
✓ calculate refractive index, critical angles and describe some uses of optical fibres
✓ define the terms principal axis, principal focus and focal length
✓ draw diagrams showing the effects of converging and diverging lenses on a beam of parallel rays and the formation of real images by a converging lens
✓ draw diagrams showing formation of a virtual image by a converging lens
✓ calculate the linear magnification of an image
✓ draw a diagram for the passage of a light ray through a prism and recall the seven colours of the visible spectrum in their correct order with respect to frequency and wavelength.
Exam-style questions
1 Figure 3.2.49 shows a ray of light PQ striking a mirror AB. The mirror AB and the mirror CD are at right angles to each other. QN is a normal to the mirror AB.
A P N
D
B C Q
50°
▲ Figure 3.2.49
a State the value of the angle of incidence of the ray PQ on the mirror AB. [2]
b Copy the diagram, and continue the ray PQ to show the path it takes after reflection
at both mirrors. [3]
c State the values of the angle of reflection at AB, the angle of incidence at CD and the angle of reflection at CD. [3]
2 a Which of the following statements is a true description of the image in a plane mirror?
A Real and larger
B Virtual and the same size C Real and the same size
D Virtual and smaller [1]
b A person stands in front of a mirror (Figure 3.2.50). How much of the mirror is used to see from eye to toes? [2]
▲ Figure 3.2.50
c A girl stands 5 m away from a large plane mirror. How far must she walk to be 2 m
away from her image? [4]
[Total: 7]
Exam-style questions
3 In Figure 3.2.51 a ray of light IO changes direction as it enters glass from air.
40°
65°
P
Q
Y X
glass
air I
R O
▲ Figure 3.2.51
a State the name given to this effect. [1]
b Identify the normal. [1]
c State whether the ray is bent towards or away from the normal in the glass. [1]
d State the value of the angle of incidence
in air. [1]
e State the value of the angle of refraction
in glass. [1]
[Total: 5]
4 Figure 3.2.52 shows rays of light in a semicircular glass block.
B A
C
▲ Figure 3.2.52
a Explain why the ray entering the glass at A is not bent as it enters. [1]
b Explain why the ray AB is reflected at B
and not refracted. [2]
c Ray CB does not stop at B. Copy the diagram and sketch its approximate path
after it leaves B. [2]
[Total: 5]
5 a Light travels up through a pond of water of critical angle 49°. Describe what happens at the surface if the angle of incidence is:
i 30° [3]
ii 60° [3]
b Calculate the critical angle for water if 4
n=3. [4]
[Total: 10]
6 a Identify the type of lens shown in
Figure 3.2.53. [1]
principal
focus focus axis
▲ Figure 3.2.53
b Copy the diagrams and complete them to show the path of the light after passing
through the lens. [3]
c Figure 3.2.54 shows an object AB 6 cm high placed 18 cm in front of a lens of focal length 6 cm. Sketch the diagram to scale and, by tracing the paths of rays from A, find the position and size of the image formed. [6]
focus 6 cm 18 cm
A
B
▲ Figure 3.2.54
[Total: 10]
7 a Three converging lenses are available, having focal lengths of 4 cm, 40 cm and 4 m, respectively. Which one would you choose
as a magnifying glass? [1]
b An object 2 cm high is viewed through a converging lens of focal length 8 cm. The object is 4 cm from the lens. By means of a ray diagram determine the position and
nature of the image. [5]
c Calculate the ratio of the image height to
object height. [2]
[Total: 8]
8 An object is placed 10 cm in front of a lens, A;
the details of the image are given below. The process is repeated for a different lens, B.
Lens A: Real, inverted, magnified and at a great distance.
Lens B: Real, inverted and same size as the object.
Determine the focal length of each lens and state whether it is converging or diverging.
[Total: 6]
9 A beam of white light strikes the face of a prism.
a Identify the effect which happens to the white light when it enters the prism. [1]
b Copy Figure 3.2.55 and draw the path taken by red and blue rays of light as they pass through the prism and onto the screen AB. [5]
white light
glass prism
A
B
▲ Figure 3.2.55
[Total: 6]
Alternative to Practical
10 You are asked to test the law of reflection.
You are given a set of pins, a plane mirror, a protractor, a ruler, some modelling clay and a large sheet of paper attached to a cork board.
a Describe a method you could use to test the law. Include a sketch of your proposed
experimental arrangement. [4]
b Draw up a table with headings showing what measurements you would take. [2]
c How would you decide if your results were in agreement with the law of reflection? [2]
d Suggest two precautions you would take to ensure accurate results. [2]
[Total: 10]
Electromagnetic spectrum
3.3
FOCUS POINTS
★ Know the order, in terms of wavelength and frequency, of the main regions of the electromagnetic spectrum.
★ Understand that all electromagnetic waves travel at the same high speed in a vacuum.
★ Know the speed of electromagnetic waves in a vacuum and that it is approximately the same in air.
★ Describe typical uses of the different regions of the electromagnetic spectrum.
★ Describe harmful effects on people of prolonged exposure to electromagnetic radiation.
Visible light forms only a small part of a very wide spectrum of electromagnetic waves, all of which travel with the speed of light in a vacuum. You will find that the properties of the different classes of waves vary with frequency from the lowest frequency radio waves through microwaves to infrared, visible and ultraviolet light, with X-rays and gamma rays at the highest frequencies.
The various electromagnetic waves have a wide range of uses from communications and cooking to food sterilisation. The energy associated with an electromagnetic wave increases with frequency, so the highest frequencies are the most dangerous. Damage from over-exposure includes burns from infrared, skin cancer and eye damage from ultraviolet and cell damage and cancer from X-rays and gamma rays.
gamma
rays X-rays ultra-
violet
infra- red
radio waves TV microwaves
light
0.01 nm 1 nm 0.1 0.4 0.7
1nm = 10–9m 1µm = 10–6m
µm µm µm 0.01 mm 1 cm 1 m 1 km
frequency increases frequency decreases
wavelength increases wavelength decreases
typical wave length:
source: radioactive
matter X-ray
tube mercury
lamp Sun electric
fire microwave
oven transmitting TV
and radio aerials radio
▲ Figure 3.3.1 The electromagnetic spectrum and sources of each type of radiation
Light is one member of the family of electromagnetic radiation which forms a continuous spectrum beyond both ends of the visible (light) spectrum. Figure 3.3.1 shows the main regions of the electromagnetic spectrum with their corresponding wavelengths.
Note that the wavelength increases from gamma rays
to radio waves while the frequency increases in the reverse direction (radio to gamma). While each type of radiation has a different source, all result from electrons in atoms undergoing an energy change and all have certain properties in common.
Properties of
electromagnetic waves
l All types of electromagnetic radiation travel through a vacuum with the same high speed as light does.
l The speed of electromagnetic waves in a vacuum is 3 × 108 m/s (300 000 km/s) and is approximately the same in air.
l They exhibit reflection, refraction and diffraction and have a transverse wave nature.
l They obey the wave equation, v = fλ, where v is the speed of light, f is the frequency of the waves and λ is the wavelength. Since v is constant in a particular medium, it follows that large f means small λ.
l They carry energy from one place to another and can be absorbed by matter to cause heating and other effects. The higher the frequency and the smaller the wavelength of the radiation, the greater is the energy carried, i.e. gamma rays are more ‘energetic’ than radio waves.
Because of its electrical origin, its ability to travel in a vacuum (e.g. from the Sun to the Earth) and its wave-like properties, electromagnetic radiation is regarded as a progressive transverse wave. The wave is a combination of travelling electric and magnetic fields. The fields vary in value and are directed at right angles to each other and to the direction of travel of the wave, as shown by the representation in Figure 3.3.2.
electric field
magnetic field
direction of travel
▲ Figure 3.3.2 An electromagnetic wave
Light waves
For the visible light part of the electromagnetic spectrum, red light has the longest wavelength, which is about 0.0007 mm (7 × 10−7 m = 0.7 µm), while violet light has the shortest wavelength of about 0.0004 mm (4 × 10−7 m = 0.4 µm). Colours between these in the spectrum of white light have intermediate values.
Since v = fλ for all waves including light, it follows that red light has a lower frequency, f, than violet light since (i) the wavelength, λ, of red light is greater and (ii) all colours travel with the same speed 3 × 108 m/s (strictly, in a vacuum). It is the frequency of light which decides its colour, rather than its wavelength which is different in different media, as is the speed (Topic 3.2.2).
Different frequencies of light travel at different speeds through a transparent medium and so are refracted by different amounts. This explains dispersion (Topic 3.2.4), in other words why the refractive index of a material depends on the wavelength of the light.
The amplitude of a light (or any other) wave is greater the higher the intensity of the source;
in the case of light the greater the intensity the brighter it is.
Visible light is the type of electromagnetic radiation used by our eyes to form images of the world around us. In addition to vision, light is used for illumination and photography (see Topic 3.2.1).
Cameras and optical instruments, from microscopes to telescopes, make use of the properties of light to form images of near and distant objects.
Worked example
The wavelength of a beam of light in air is 5 × 10−7 m.
Calculate its frequency.
Rearrange the equation v = fλ to give f = v λ. Taking v = 3 × 108 m/s, then
f = 3 × 108 m/s / 5 × 10−7 m = 6 × 1014 Hz
Now put this into practice
1 The wavelength of a beam of light in air is 6 × 10−7 m.
Calculate its frequency.
2 The frequency of a beam of infrared radiation in air is 4.0 × 1014 Hz. Calculate its wavelength.
Radio waves
Test yourself
1 Give the approximate wavelength in micrometres (µm) of
a red light b violet light.
2 Which of the following types of radiation has a the longest wavelength
b the highest frequency?
A ultraviolet B radio waves C light D X-rays
Infrared radiation
Our bodies detect infrared radiation (IR) by its heating effect on the skin. It is sometimes called
‘radiant heat’ or ‘heat radiation’.
Anything which is hot but not glowing, i.e.
below 500°C, emits IR alone. At about 500°C a body becomes red hot and emits red light as well as IR – the heating element of an electric fire, a toaster or an electric grill are examples. At about 1500°C, things such as lamp filaments are white hot and radiate IR and white light, i.e. all the colours of the visible spectrum.
Infrared is also used in thermal imaging cameras, which show hot spots and allow images to be taken in the dark. Infrared sensors are used on satellites and aircraft for weather forecasting, monitoring of land use (Figure 3.3.3), assessing energy loss from buildings and locating victims of earthquakes. One type of intruder alarm activates an alarm when its sensor detects the infrared radiation emitted by a nearby moving body. An alternative type uses a transmitter to send an infrared beam to a receiver.
When the path of the beam is broken by an intruder, an alarm is activated.
The remote control for an electronic device contains a small infrared transmitter to send signals to the device, such as a television or DVD player.
These are short range communication applications.
Infrared is also used to carry data in long range optical fibre communication systems (Topic 3.2.2).
Infrared radiation can cause burns to the skin and eye damage if the intensity is high.
▲ Figure 3.3.3 Infrared aerial photograph in false colour, with red showing vegetation
Ultraviolet radiation
Ultraviolet (UV) rays have shorter wavelengths than light. They cause sun tan and produce vitamins in the skin but too high an exposure can be harmful.
Ultraviolet radiation causes fluorescent paints and clothes washed in some detergents to fluoresce.
They glow by re-radiating as light the energy they absorb as UV. This effect may be used in security marking to verify ‘invisible’ signatures on bank documents and to detect fake bank notes. Water treatment plants often use UV radiation to sterilise water because the energy of UV radiation is high enough energy to kill bacteria.
Radio waves
Radio waves have the longest wavelengths in the electromagnetic spectrum. They are radiated from aerials and used to carry sound, pictures and other information over long distances.
Long, medium and short waves (wavelengths of 2 km to 10 m)
These diffract round obstacles so can be received even when hills are in their way (Figure 3.3.4a).
They are also reflected by layers of electrically charged particles in the upper atmosphere (the ionosphere), which makes long-distance radio reception possible (Figure 3.3.4b).
a Diffraction of radio waves
transmitter receiver
ionosphere b Reflection of radio waves
▲ Figure 3.3.4
VHF (very high frequency) and UHF (ultra high frequency) waves (wavelengths of 10 m to 10 cm)
These shorter wavelength radio waves need a clear, straight-line path to the receiver. They are not reflected by the ionosphere. They are used for local radio and for television transmissions.
Astronomers use radio telescopes to pick up radio signals from stars and galaxies to gain information about the Universe which cannot be obtained from optical telescopes.
Microwaves
Microwaves have wavelengths of a few cm. They are used for international telecommunications and direct broadcast satellite television relay via geostationary satellites and for mobile phone networks via microwave aerial towers and low-orbit satellites (Topic 1.5.1). The microwave signals are transmitted through the ionosphere by dish aerials, amplified by the satellite and sent back to a dish aerial in another part of the world. Some satellite phones also use low-orbit artificial satellites.
Microwaves are also used in wireless applications,
of electronic devices from mobile phones to entertainment systems.
Microwaves can be used for cooking in a
microwave oven since they cause water molecules in the moisture of the food to vibrate vigorously at the frequency of the microwaves. As a result, heating occurs inside the food which cooks itself.