FOCUS POINT
SECTION 3 Waves
3.2.2 Refraction of light
3.2.2 Refraction of light
Although light travels in straight lines in a transparent material, such as air, if it passes into a different material, such as water, it changes direction at the boundary between the two, i.e. it is bent. The bending of light when it passes from one material (called a medium) to another is called refraction. It causes effects such as the coin trick.
Terms used in connection with refraction are shown in Figure 3.2.21. The perpendicular to the boundary between two mediums is called the normal. The angle of incidence i is the angle between the incident ray and the normal; similarly, the angle of refraction r is the angle between the refracted ray and the normal.
Key definitions
Angle of refraction angle between refracted ray and the normal to a surface
Facts about refraction
(i) A ray of light is bent towards the normal when it enters an optically denser medium at an angle, for example from air to glass as in Figure 3.2.21.
So the angle of refraction r is smaller than the angle of incidence i.
(ii) A ray of light is bent away from the normal when it enters an optically less dense medium, for example from glass to air.
(iii) A ray emerging from a parallel-sided block is parallel to the ray entering, but is displaced sideways, like the ray in Figure 3.2.21a.
(iv) A ray travelling along the normal direction at a boundary is not refracted (Figure 3.2.21b).
Note that ‘optically denser’ means having a greater refraction effect; the actual density may or may not be greater.
air
normal
glass
normal i
r a
normal
glass
air b
▲ Figure 3.2.21 Refraction of light in glass
Practical work
Refraction in glass Safety
l Take care as the filament lamp and shield will get hot when in use.
Shine a ray of light at an angle onto a glass block (which has its lower face painted white or is frosted), as in Figure 3.2.22. Draw the outline ABCD of the block on the sheet of paper under it.
Mark the positions of the various rays in air and in glass.
Remove the block and draw the normals on the paper at the points where the ray enters side AB (see Figure 3.2.22) and where it leaves side CD.
D
C glass block shield
lampand stand
single slit normal
A
B
sheet of paper
▲ Figure 3.2.22
10 What two things happen to the light falling on AB?
11 When the ray enters the glass at AB, is it bent towards or away from the part of the normal in the block?
12 How is it bent at CD?
13 What can you say about the direction of the ray falling on AB and the direction of the ray leaving CD?
14 What happens if the ray hits AB at right angles?
Refractive index
Light is refracted because its speed changes when it enters another medium. An analogy helps to explain why.Suppose three people A, B, C are marching in line, with hands linked, on a good road surface. If they approach marshy ground at an angle (see Figure 3.2.25), person A is slowed down first, followed by B and then C. This causes the whole line to swing round and change its direction of motion.
In air (and a vacuum) light travels at
300 000 km/s (3 × 108 m/s); in glass its speed falls to 200 000 km/s (2 × 108 m/s).
We define the refractive index, n, as the ratio of the sine of the angle of incidence to the sine of the angle of refraction.
Key definition
Refractive index n n= i r sin sin
The greater the refractive index of the medium, the more the light is bent.
road
marsh A
B
C C
C B
B A
A
Going further
Real and apparent depth
Rays of light from a point O on the bottom of a pool are refracted away from the normal at the water surface because they are passing into an optically less dense medium, i.e. air (Figure 3.2.23). On entering the eye, they appear to come from a point I that is above O; I is the virtual image of O formed by refraction. The apparent depth of the pool is less than its real depth. Similarly, rays from the submerged part of the pencil in Figure 3.2.24 are refracted at the water surface.
real
depth apparent
depth
water I
O
▲ Figure 3.2.23 A pool of water appears shallower than it is.
▲ Figure 3.2.24 A pencil placed in water seems to bend
3.2.2 Refraction of light
We saw earlier (Topic 3.1) that water waves are refracted when their speed changes. The change in the direction of travel of a light ray when its speed changes on entering another medium suggests that light may also be a type of wave motion.
Worked example
The refractive index for a certain glass is 1.6.
Calculate the angle of refraction for an angle of incidence of 24°.
n i
r sin
=sin so sin r = sin i/n
= sin 24°/1.6
= 0.41/1.6 = 0.25 and r= 15°
Now put this into practice
1 The refractive index for a certain glass is 1.5.
Calculate the angle of refraction for an angle of incidence of 30°.
Critical angle
When light passes at small angles of incidence from an optically dense to a less dense medium, such as from glass to air, there is a strong refracted ray and a weak ray reflected back into the denser medium (Figure 3.2.26a). As well as refraction, some internal reflection occurs. Increasing the angle of incidence increases the angle of refraction.
air glass a
air glass
c c
c critical angle b
air glass c
▲ Figure 3.2.26
At a certain angle of incidence, called the critical angle, c, the angle of refraction is 90°
(Figure 3.2.26b) and the refracted ray passes along the boundary between the two media.
For angles of incidence greater than c, the refracted ray disappears and all the incident light is reflected inside the denser medium (Figure 3.2.26c).
The light does not cross the boundary and is said to undergo total internal reflection.
On a hot day the road ahead may appear to shimmer with water. The layers of air close to the surface of the road are hotter and less dense than those above and refraction of sunlight occurs. When the critical angle of incidence is reached, the light undergoes total internal reflection, resulting in a mirage which disappears as you move towards it.
Key definitions
Critical angle c angle of incidence which produces an angle of refraction of 90°
Total internal reflection occurs when a light ray does not cross the boundary between two media; it is totally reflected at the boundary
Practical work
Critical angle of glass
Place a semicircular glass block on a sheet of paper (Figure 3.2.27), and draw the outline LOMN where O is the centre and ON the normal at O to LOM. Direct a narrow ray (at an angle of about 30° to the normal ON) along a radius towards O. The ray is not refracted at the curved surface. Note the refracted ray emerging from LOM into the air and also the weak internally reflected ray in the glass.
ray of light
N
semicircular glass block
angle of incidence sheet of paper L
M O
▲ Figure 3.2.27
Slowly rotate the paper so that the angle of incidence on LOM increases until total internal reflection just occurs. Mark the incident ray.
Measure the angle of incidence; this is the critical angle.
15 Why is the ray not refracted at the curved surface?
16 What is the value you obtain for the critical angle?
17 Name the rays at O when the angle of incidence is less than the critical angle.
Refractive index and critical angle
From Figure 3.2.26b and the definition of refractive index:
n
c c
sine of angle between ray in air and normal sine of angle between ray in glass and normal sin 90
sin
sin1 (because sin 90 1)
=
= °
= ° =
So, if n =3/2, then sin c =2/3 and c must be 42°.
Worked example
If the critical angle for diamond is 24°, calculate its refractive index.
c
n c
critical angle, 24 sin 24 0.4
sin 90 sin
1 sin 24 1
0.4 2.5
= °
° =
= ° =
°
= =
Now put this into practice
1 The critical angle for a transparent material is 32°.
Calculate its refractive index.
2 The refractive index of a transparent material is 1.7.
Work out its critical angle.
Multiple images in a mirror
An ordinary mirror silvered at the back forms several images of one object, because of multiple reflections inside the glass (Figure 3.2.28 opposite).
These blur the main image I (which is formed by one reflection at the silvering), especially if the glass is thick. The problem is absent in front-silvered mirrors but such mirrors are easily damaged.
3.2.2 Refraction of light
O object
I1 I I2
main image
silvering glass
▲ Figure 3.2.28a Multiple reflections in a mirror
▲ Figure 3.2.28b The multiple images in a mirror cause blurring.
Totally reflecting prisms
The defects of mirrors are overcome if 45° right- angled glass prisms are used. The critical angle of ordinary glass is about 42° and a ray falling normally on face PQ of such a prism (Figure 3.2.29a) hits face PR at 45°. Total internal reflection occurs and the ray is turned through 90°. Totally reflecting prisms replace mirrors in good periscopes.
Light can also be reflected through 180° by a prism (Figure 3.2.29b); this happens in binoculars.
Q R
P
45°
45°
45°
a
b
▲ Figure 3.2.29 Reflection of light by a prism
Light pipes and optical fibres
Light can be trapped by total internal reflection inside a bent glass rod and piped along a curved path (Figure 3.2.30). A single, very thin glass fibre, an optical fibre, behaves in the same way.
▲ Figure 3.2.30 Light travels through a curved glass rod or optical fibre by total internal reflection.
If several thousand such fibres are taped together, a flexible light pipe is obtained that can be used, for example, by doctors as an endoscope (Figure 3.2.31a), to obtain an image from inside the body (Figure 3.2.31b), or by engineers to light up some awkward spot for inspection.
▲ Figure 3.2.31a Endoscope in use
▲ Figure 3.2.31b Trachea (windpipe) viewed by an
Increasingly, optical fibres are being used to carry telephone, high-speed broadband internet and cable TV signals as pulses of visible or infrared light. The advantages over copper cables for telecommunication purposes are that the use of light allows information to be transmitted at a higher rate and the data is more secure because
the cables are unaffected by electronic interference.
They can be used over longer distances (since they have lower power loss), are made of cheaper material and, as they are lighter and thinner, are easier to handle and install. However, they are not as strong as copper cables and can break if bent too much.
Test yourself
8 Figure 3.2.32 shows a ray of light entering a rectangular block of glass.
a Copy the diagram and draw the normal at the point of entry.
b Sketch the approximate path of the ray through the block and out of the other side.
▲ Figure 3.2.32
9 Draw two rays from a point on a fish in a stream to show where someone on the bank will see the fish.
Where must the person aim to spear the fish?
10 Which diagram in Figure 3.2.33 shows the ray of light refracted correctly?
B air water
air
D water glass glass
C
air glass
A
▲ Figure 3.2.33
11 Copy Figures 3.2.34a and 3.2.34b and complete the paths of the rays through the glass prisms.
glass 60°
60° a
air
glass
45°
b
▲ Figure 3.2.34