FOCUS POINT
SECTION 3 Waves
3.2.1 Reflection of light
FOCUS POINTS
★ Define and understand the terms normal, angle of incidence and angle of reflection.
★ Describe how an optical image is formed by a plane mirror and give its characteristics.
★ For reflection, know the relationship between angle of incidence and angle of reflection.
★ Construct, measure and calculate reflection by plane mirrors.
In the last topic you learnt about some of the general properties of waves by studying the behaviour of water waves. Water waves are transverse waves but so too are light waves and you can expect them both to have similar properties. In this topic you will explore how light is reflected by a plane surface. Reflection is made use of in mirrors and instruments such as a periscope. Reflection in a mirror produces an apparent image of an object behind the surface of the mirror; this virtual image is the same size as the object and the same distance from the mirror as the object but has left and right switched.
Sources of light
You can see an object only if light from it enters your eyes. Some objects such as the Sun, electric lamps and candles make their own light. We call these luminous sources.
Most things you see do not make their own light but reflect it from a luminous source. They are non- luminous objects. This page, you and the Moon are examples. Figure 3.2.1 shows some others.
non-luminous objects reflecting light
luminous source emitting light
▲ Figure 3.2.1 Luminous and non-luminous objects
Luminous sources radiate light when their atoms become ‘excited’ as a result of receiving energy.
In a light bulb, for example, the energy comes from electricity. The ‘excited’ atoms give off their light haphazardly in most luminous sources.
A light source that works differently is the laser, invented in 1960. In laser light sources the excited atoms act together and emit a narrow, very bright beam of light. The laser has a host of applications.
It is used in industry to cut through plate metal, in scanners to read bar codes at shop and library check- outs, in CD players, in optical fibre telecommunication systems, in delicate medical operations on the eye or inner ear (for example Figure 3.2.2), in printing and in surveying and range-finding.
▲ Figure 3.2.2 Laser surgery in the inner ear
Rays and beams
Sunbeams streaming through trees (Figure 3.2.3) and light from a cinema projector on its way to the screen both suggest that light travels in straight lines. The beams are visible because dust particles in the air reflect light into our eyes.
The direction of the path in which light is travelling is called a ray and is represented in diagrams by a straight line with an arrow on it. A beam is a stream
of light and is shown by a number of rays, as in Figure 3.2.4. A beam may be parallel, diverging (spreading out) or converging (getting narrower).
▲ Figure 3.2.3 Light travels in straight lines.
converging diverging
ray
parallel
▲ Figure 3.2.4 Beams of light
Practical work
The pinhole camera Safety
l Take care when using the needle to make the pinhole.
A simple pinhole camera is shown in Figure 3.2.5a. Make a small pinhole in the centre of the black paper. Half darken the room. Hold the box at arm’s length so that the pinhole end is nearer to and about 1 metre from a luminous object, such as a carbon filament lamp or
(an image is a likeness of an object and need not be an exact copy). Make several small pinholes round the large hole (Figure 3.2.5b), and view the image again.
The formation of an image is shown in Figure 3.2.6.
black paper round hole in box
small pinhole
lid
box
screen (greaseproof paper over square hole in box) a
large pinhole b
small pinhole
black paper
▲ Figure 3.2.5 A
B object
pinhole
image B'
A'
▲ Figure 3.2.6 Forming an image in a pinhole camera
1 Can you see three ways in which the image differs from the object?
2 What is the effect of moving the camera closer to the object?
3 Make the pinhole larger. What happens to thea brightness
b sharpness
3.2.1 Reflection of light
Going further
Shadows
Shadows are formed for two reasons. First, because some objects, which are said to be opaque, do not allow light to pass through them. Secondly, light travels in straight lines.
The sharpness of the shadow depends on the size of the light source. A very small source of light, called a point source, gives a sharp shadow which is equally dark all over. This may be shown as in Figure 3.2.7a where the small hole in the card acts as a point source.
small hole card
100 watt lamp
to mains supply
metal ball
screen sharp shadow a
penumbra umbra b
▲ Figure 3.2.7 Forming a shadow
If the card is removed the lamp acts as a large or extended source (Figure 3.2.7b). The shadow is then larger and has a central dark region, the umbra, surrounded by a ring of partial shadow, the penumbra. You can see by the rays that some light reaches the penumbra, but none reaches the umbra.
Speed of light
Proof that light travels very much faster than sound is provided by a thunderstorm. The flash of lightning is seen before the thunder is heard. The length of the time lapse is greater the further the observer is from the storm.
The speed of light has a definite value; light does not travel instantaneously from one point to another but takes a certain, very small time. Its speed is about 1 million times greater than that of sound.
Reflection of light
If we know how light behaves when it is reflected, we can use a mirror to change the direction in which the light is travelling. This happens when a mirror is placed at the entrance of a concealed drive to give warning of approaching traffic, for example.
An ordinary mirror is made by depositing a thin layer of silver on one side of a piece of glass and protecting it with paint. The silver – at the back of the glass – acts as the reflecting surface. A plane mirror is produced when the reflecting surface is flat.
Law of reflection
Terms used in connection with reflection are shown in Figure 3.2.8. The perpendicular to the mirror at the point where the incident ray strikes is called the normal. Note that the angle of incidence i is the angle between the incident ray and the normal;
similarly, the angle of reflection r is the angle between the reflected ray and the normal.
Key definitions
Normal line which is perpendicular to a surface Angle of incidence angle between incident ray and the normal to a surface
Angle of reflection angle between reflected ray and the normal to a surface
Law of reflection the angle of incidence is equal to the angle of reflection
plane mirror
i r
incident ray
normal reflected
ray
▲ Figure 3.2.8 Reflection of light by a plane mirror
The law of reflection states:
The angle of incidence is equal to the angle of reflection.
The incident ray, the reflected ray and the normal all lie in the same plane. (This means that they
Periscope
A simple periscope consists of a tube containing two plane mirrors, fixed parallel to and facing each other.
Each makes an angle of 45° with the line joining them (Figure 3.2.10). Light from the object is turned through 90° at each reflection and an observer is able to see over a crowd, for example (Figure 3.2.11), or over the top of an obstacle.
obstacle
45°
45°
▲ Figure 3.2.10 Action of a simple periscope
▲ Figure 3.2.11 Periscopes being used by people in a crowd.
In more elaborate periscopes like those used in submarines, prisms replace mirrors (see p. 147).
Make your own periscope from a long, narrow cardboard box measuring about 40 cm × 5 cm × 5 cm (such as one in which aluminium cooking foil or clingfilm is sold), two plane mirrors (7.5 cm × 5 cm) and sticky tape. When you have got it to work, make modifications that turn it into a ‘see-back-o-scope’,
Practical work
Reflection by a plane mirror Safety
l Take care as the filament lamp and shield will get hot when in use.
Draw a line AOB on a sheet of paper and using a protractor mark angles on it. Measure them from the perpendicular ON, which is at right angles to AOB. Set up a plane (flat) mirror with its reflecting surface on AOB.
Shine a narrow ray of light along, say, the 30°
line onto the mirror (Figure 3.2.9).
shield
lamp and stand
single slit
A
B O N
15°30°45°60°75°
sheet of paper
plane mirror
▲ Figure 3.2.9
Mark the position of the reflected ray, remove the mirror and measure the angle between the reflected ray and ON. Repeat for rays at other angles.
4 In the experiment what can you conclude about the incident and reflected rays?
5 The silver surface on a mirror is usually on the back surface of the glass. How might this affect the accuracy of your measurements?
3.2.1 Reflection of light
Going further
Regular and diffuse reflection
If a parallel beam of light falls on a plane mirror it is reflected as a parallel beam (Figure 3.2.12a) and regular reflection occurs. Most surfaces, however, reflect light irregularly and the rays in an incident parallel beam are reflected in many directions (Figure 3.2.12b), this is known as diffuse reflection.
plane mirror a
normal
normal
‘rough’ surface b
▲ Figure 3.2.12
Plane mirrors
When you look into a plane mirror on the wall of a room you see an image of the room behind the mirror; it is as if there were another room.
Restaurants sometimes have a large mirror on one wall just to make them look larger. You may be able to say how much larger after the next experiment.
The position of the image formed by a mirror
Practical work
Position of the image
glass (microscope slide)
white paper arrow
dark surface
Plasticine
block to support glass vertically
O I
▲ Figure 3.2.13
Support a piece of thin glass on the bench, as in Figure 3.2.13. It must be vertical (at 90° to the bench). Place a small paper arrow, O, about 10 cm from the glass. The glass acts as a poor mirror and an image of O will be seen in it; the darker the bench top, the brighter the image will be.
Lay another identical arrow, I, on the bench behind the glass; move it until it coincides with the image of O.
6 How do the sizes of O and its image compare?
7 Imagine a line joining them. What can you say about it?
8 Measure the distances of the points of O and I from the glass along the line joining them.
How do the distances compare?
9 Try placing O at other distances and
orientations. How does the orientation of the image relative to the object change if the arrow is turned through 45°?
Going further
Kaleidoscope
▲ Figure 3.2.16 A kaleidoscope produces patterns using
Check that the images in Figure 3.2.16 have the expected properties of an image in a plane mirror.
To see how a kaleidoscope works, draw on a sheet of paper two lines at right angles to one another. Using different coloured pens or pencils, draw a design between them (Figure 3.2.17a). Place a small mirror along each line and look into the mirrors (Figure 3.2.17b).
You will see three reflections which join up to give a circular pattern. If you make the angle between the mirrors smaller, more reflections appear but you always get a complete design.
In a kaleidoscope the two mirrors are usually kept at the same angle (about 60°) and different designs are made
Real and virtual images
A real image is one which can be produced on a screen (as in a pinhole camera) and is formed by rays that actually pass through the screen.
A virtual image cannot be formed on a screen.
The virtual image is produced by rays which seem to come from it but do not pass through it.
The image in a plane mirror is virtual. Rays from a point on an object are reflected at the mirror and appear to our eyes to come from a point behind the mirror where the rays would intersect when extrapolated backwards (Figure 3.2.14). IA and IB are construction lines and are shown as broken lines.
I
N
A B
O
virtual rays
real rays
▲ Figure 3.2.14 A plane mirror forms a virtual image.
Going further
Lateral inversion
If you close your left eye, your image in a plane mirror seems to close the right eye. In a mirror image, left and right are interchanged and the image appears to be laterally inverted. The effect occurs whenever an image is formed by one reflection and is very evident if print is viewed in a mirror (Figure 3.2.15). What happens if two reflections occur, as in a periscope?
▲ Figure 3.2.15 The image in a plane mirror is laterally inverted.
Properties of the image
The image in a plane mirror is
(i) as far behind the mirror as the object is in front, with the line joining the same points on object and image being perpendicular to the mirror (ii) the same size as the object
(iii) virtual.
3.2.1 Reflection of light
Test yourself
1 How would the size and brightness of the image formed by a pinhole camera change if the camera were made longer?
2 What changes would occur in the image if the single pinhole in a camera were replaced by a four pinholes close together
b a hole 1 cm wide?
3 In Figure 3.2.18 the completely dark region on the screen is
A PQ B PR C QR D QS
4 When watching a distant firework display do you see the cascade of lights before or after hearing the associated bang? Explain your answer.
object lamp
screen P Q R S
▲ Figure 3.2.18 sheet of paper
▲ Figure 3.2.17a
mirror
paper
mirror
▲ Figure 3.2.17b
Now make a kaleidoscope using a cardboard tube (from half a kitchen roll), some thin card, greaseproof paper, clear sticky tape, small pieces of different coloured cellophane and two mirrors (10 cm × 3 cm) or a single plastic mirror (10 cm × 6 cm) bent to form two mirrors at 60° to each other, as shown in Figure 3.2.17c.
card with central pinhole mirrors at 60°
coloured cellophane
cardboard tube greaseproof paper
▲ Figure 3.2.17c