Connexions module: m40062
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Geometrical optics: Reflection
∗
Free High School Science Texts Project
This work is produced by The Connexions Project and licensed under the
Creative Commons Attribution License †
1 Reection
When you smile into a mirror, you see your own face smiling back at you. This is caused by the reection
of light rays on the mirror. Reection occurs when a light ray bounces o a surface.
1.1 Terminology
In Transverse Pulses1 and Transverse Waves2 we saw that when a pulse or wave strikes a surface it is
reected. This means that waves bounce o things. Sound waves bounce o walls, light waves bounce o
mirrors, radar waves bounce o aeroplanes and it can explain how bats can y at night and avoid things as
thin as telephone wires. The phenomenon of reection is a very important and useful one.
We will use the following terminology. The incoming light ray is called the incident ray. The light
ray moving away from the surface is the reected ray. The most important characteristic of these rays
is their angles in relation to the reecting surface. These angles are measured with respect to the normal
of the surface. The normal is an imaginary line perpendicular to the surface. The angle of incidence,
θi is measured between the incident ray and the surface normal. The angle of reection, θr is measured
between the reected ray and the surface normal. This is shown in Figure 1.
When a ray of light is reected, the reected ray lies in the same plane as the incident ray and the normal.
This plane is called the plane of incidence and is shown in Figure 2.
Figure 1: The angles of incidence and reection are measured with respect to the surface normal.
∗ Version
1.1: Aug 5, 2011 9:30 am GMT-5
† http://creativecommons.org/licenses/by/3.0/
1 "Transverse Pulses - Grade 10" <http://cnx.org/content/m35714/latest/>
2 "Transverse Waves - Grade 10" <http://cnx.org/content/m32635/latest/>
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Figure 2: The plane of incidence is the plane including the incident ray, reected ray, and the surface
normal.
1.2 Law of Reection
The Law of Reection
states that the angles of incidence and reection are always equal and that the
reected ray always lies in the plane of incidence.
Denition 1: Law of Reection
The Law of Reection states that the angle of incidence is equal to the angle of reection.
(1)
θi = θr
The simplest example of the law of incidence is if the angle of incidence is 0◦ . In this case, the angle of
reection is also 0◦ . You see this when you look straight into a mirror.
Figure 3: When a wave strikes a surface at right angles to the surface, then the wave is reected directly
back.
If the angle of incidence is not 0◦ , then the angle of reection is also not 0◦ . For example, if a light strikes
a surface at 60◦ to the surface normal, then the angle that the reected ray makes with the surface normal
is also 60◦ as shown in Figure 4.
Figure 4: Ray diagram showing angle of incidence and angle of reection. The Law of Reection states
that when a light ray reects o a surface, the angle of reection θr is the same as the angle of incidence
θi .
Exercise 1: Law of Reection
(Solution on p. 6.)
An incident ray strikes a smooth reective surface at an angle of 33◦ to the surface normal.
Calculate the angle of reection.
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1.3 Types of Reection
The Law of Reection holds for every light ray. Does this mean that when parallel rays approach a surface,
the reected rays will also be parallel? This depends on the texture of the reecting surface.
(a)
(b)
Figure 5: Specular and diuse reection.
1.3.1 Specular Reection
Figure 5(a) shows a surface that is at and even. Parallel incident light rays hit the smooth surface and
parallel reected light rays leave the surface. This type of reection is called specular reection. Specular
reection occurs when rays are reected from a smooth, shiny surface. The normal to the surface is the
same at every point on the surface. Parallel incident rays become parallel reected rays. When you look in
a mirror, the image you see is formed by specular reection.
1.3.2 Diuse Reection
Figure 5(b) shows a surface with bumps and curves. When multiple rays hit this uneven surface, diuse
reection occurs. The incident rays are parallel but the reected rays are not. Each point on the surface
has a dierent normal. This means the angle of incidence is dierent at each point. Then according to the
Law of Reection, each angle of reection is dierent. Diuse reection occurs when light rays are reected
from bumpy surfaces. You can still see a reection as long as the surface is not too bumpy. Diuse reection
enables us to see all objects that are not sources of light.
1.3.2.1 Experiment : Specular and Diuse Reection
A bouncing ball can be used to demonstrate the basic dierence between specular and diuse reection.
Aim:
To demonstrate and compare specular and diuse reection.
Apparatus:
You will need:
1. a small ball (a tennis ball or a table tennis ball is perfect)
2. a smooth surface, like the oor inside the classroom
3. a very rough surface, like a rocky piece of ground
Method:
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2.
3.
4.
4
Bounce the ball on the smooth oor and observe what happens.
Bounce the ball on the rough ground oor and observe what happens.
What do you observe?
What is the dierence between the two surfaces?
Conclusions:
You should have seen that the ball bounces (is reected o the oor) in a predictable manner o the
smooth oor, but bounces unpredictably on the rough ground.
The ball can be seen to be a ray of light and the oor or ground is the reecting surface. For specular
reection (smooth surface), the ball bounces predictably. For diuse reection (rough surface), the ball
bounces unpredictably.
1.3.2.2 Reection
1. The diagram shows a curved surface. Draw normals to the surface at the marked points.
Figure 6
Click here for the solution.3
2. Which of the points, AH, in the diagram, correspond to the following:
a.
b.
c.
d.
e.
normal
angle of incidence
angle of reection
incident ray
reected ray
Figure 7
Click here for the solution.4
3. State the Law of Reection. Draw a diagram, label the appropriate angles and write a mathematical
expression for the Law of Reection.
Click here for the solution.5
4. The diagram shows an incident ray I . Which of the other 5 rays (A, B, C, D, E) best represents the
reected ray of I ?
3 http://www.fhsst.org/lrz
4 http://www.fhsst.org/lru
5 http://www.fhsst.org/lrJ
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Figure 8
5.
6.
7.
8.
9.
Click here for the solution.6
A ray of light strikes a surface at 15◦ to the surface normal. Draw a ray diagram showing the incident
ray, reected ray and surface normal. Calculate the angles of incidence and reection and ll them in
on your diagram.
Click here for the solution.7
A ray of light leaves a surface at 65◦ to the surface. Draw a ray diagram showing the incident ray,
reected ray and surface normal. Calculate the angles of incidence and reection and ll them in on
your diagram.
Click here for the solution.8
Explain the dierence between specular and diuse reection.
Click here for the solution.9
We see an object when the light that is reected by the object enters our eyes. Do you think the
reection by most objects is specular reection or diuse reection? Explain.
Click here for the solution.10
A beam of light (for example from a torch) is generally not visible at night, as it travels through air.
Try this for yourself. However, if you shine the torch through dust, the beam is visible. Explain why
this happens.
Click here for the solution.11
6 http://www.fhsst.org/lrS
7 http://www.fhsst.org/lrh
8 http://www.fhsst.org/lYg
9 http://www.fhsst.org/lYl
10 http://www.fhsst.org/lYi
11 http://www.fhsst.org/lY3
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Solutions to Exercises in this Module
Solution to Exercise (p. 2)
Step 1. We are given the angle between the incident ray and the surface normal. This is the angle of incidence.
We are required to calculate the angle of reection.
Step 2. We can use the Law of Reection, which states that the angle of incidence is equal to the angle of
reection.
Step 3. We are given the angle of incidence to be 33◦ . Therefore, the angle of reection is also 33◦ .
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