Lecture Notes on Geometrical Optics (PHY102)
Geometrical Optics
There are three ways in which light can travel from one source to another location. It can come
directly from the source through empty space, such as from the Sun to Earth. Light can also
travel through various media, such as air and glass, to the person. Light can also arrive after
being reflected, such as a mirror. In all of these cases, light is modelled as traveling in straight
lines called rays. Light may change direction when it encounters objects (such as a mirror) or
passing from one material to another (such as in passing from air to glass), but it then continues
in a straight line or as a ray. The word ray comes from mathematics and here it means a straight
line that originates at some point. It is acceptable to visualize light rays as laser rays (or even
science fiction depictions of ray guns).
Experiments, as well as our own experiences, show that when light interacts with objects
several times as large as its wavelength, it travels in straight lines and acts like a ray. Its wave
characteristics are not pronounced in such situations. Since the wavelength of light is less
than a micron (a thousandth of a millimeter), it acts like a ray in many common situations in
which it encounters objects larger than a micron. For example, when light encounters
anything we can observe with unaided eyes, such as a mirror, it acts like a ray, with only
subtle wave characteristics.
Since light moves in straight lines, changing directions when it interacts with materials, it is
described by geometry and simple trigonometry. This part of optics, where the ray aspect of
light dominates, is therefore called geometric optics. Two laws govern how light changes
direction when it interacts with matter. These are the law of reflection. Situations in which
light bounces off matter, and the law of refraction, for situations in which light passes through
matter.
The Law of Reflection
The law of reflection is illustrated in the diagram below, which also shows how the angles are
measured relative to the perpendicular to the surface at the point where the light ray strikes.
We expect to see reflections from smooth surfaces, but b illustrates how a rough surface reflects
light. Since the light strikes different parts of the surface at different angles, it is reflected in
many different directions, or diffused. Diffused light is what allows us to see a sheet of paper
from any angle, as illustrated in c. Many objects, such as people, clothing, leaves, and walls,
have rough surfaces and can be seen from all sides. A mirror, on the other hand, has a smooth
surface (compared with the wavelength of light) and reflects light at specific angles, as
illustrated in d.
, (a) (b)
(c) (d)
(a) The law of reflection states that the angle of reflection equals to the angle of incidence 𝜃" =
𝜃$ . The angles are measured relative to the perpendicular of the surface at the point where the
ray strikes the surface.
(b) Light is diffused when it reflects from a rough surface. Here, many parallel rays are incident,
but they are reflected at many different angles since the surface is rough.
(c) When a sheet of paper is illuminated with many parallel incident rays, it can be seen at
different angles, because its surface is rough and diffuses the light.
(d) A mirror illuminated by many parallel rays reflects them in only one direction since its
surface is very smooth. Only the observer at a particular angle will see the reflected light.
The laws of reflection can be summarized as follows
• The incident ray, the reflected ray and the normal at the point of incidence all lie in the
same plane.
• The angle of incidence (i) is equal to the angle of reflection (r).
Law of Refraction
The change in direction of a light ray depends on how the speed of light changes when it crosses
from one medium to another (Figure E). The speed of light is greater in medium 1 than in
medium 2 in the situations shown here. (a) A ray of light moves closer to the perpendicular
when it slows down. This is analogous to what happens when a lawn mower goes from a
footpath to grass. (b) A ray of light moves away from the perpendicular when it speeds up.
Geometrical Optics
There are three ways in which light can travel from one source to another location. It can come
directly from the source through empty space, such as from the Sun to Earth. Light can also
travel through various media, such as air and glass, to the person. Light can also arrive after
being reflected, such as a mirror. In all of these cases, light is modelled as traveling in straight
lines called rays. Light may change direction when it encounters objects (such as a mirror) or
passing from one material to another (such as in passing from air to glass), but it then continues
in a straight line or as a ray. The word ray comes from mathematics and here it means a straight
line that originates at some point. It is acceptable to visualize light rays as laser rays (or even
science fiction depictions of ray guns).
Experiments, as well as our own experiences, show that when light interacts with objects
several times as large as its wavelength, it travels in straight lines and acts like a ray. Its wave
characteristics are not pronounced in such situations. Since the wavelength of light is less
than a micron (a thousandth of a millimeter), it acts like a ray in many common situations in
which it encounters objects larger than a micron. For example, when light encounters
anything we can observe with unaided eyes, such as a mirror, it acts like a ray, with only
subtle wave characteristics.
Since light moves in straight lines, changing directions when it interacts with materials, it is
described by geometry and simple trigonometry. This part of optics, where the ray aspect of
light dominates, is therefore called geometric optics. Two laws govern how light changes
direction when it interacts with matter. These are the law of reflection. Situations in which
light bounces off matter, and the law of refraction, for situations in which light passes through
matter.
The Law of Reflection
The law of reflection is illustrated in the diagram below, which also shows how the angles are
measured relative to the perpendicular to the surface at the point where the light ray strikes.
We expect to see reflections from smooth surfaces, but b illustrates how a rough surface reflects
light. Since the light strikes different parts of the surface at different angles, it is reflected in
many different directions, or diffused. Diffused light is what allows us to see a sheet of paper
from any angle, as illustrated in c. Many objects, such as people, clothing, leaves, and walls,
have rough surfaces and can be seen from all sides. A mirror, on the other hand, has a smooth
surface (compared with the wavelength of light) and reflects light at specific angles, as
illustrated in d.
, (a) (b)
(c) (d)
(a) The law of reflection states that the angle of reflection equals to the angle of incidence 𝜃" =
𝜃$ . The angles are measured relative to the perpendicular of the surface at the point where the
ray strikes the surface.
(b) Light is diffused when it reflects from a rough surface. Here, many parallel rays are incident,
but they are reflected at many different angles since the surface is rough.
(c) When a sheet of paper is illuminated with many parallel incident rays, it can be seen at
different angles, because its surface is rough and diffuses the light.
(d) A mirror illuminated by many parallel rays reflects them in only one direction since its
surface is very smooth. Only the observer at a particular angle will see the reflected light.
The laws of reflection can be summarized as follows
• The incident ray, the reflected ray and the normal at the point of incidence all lie in the
same plane.
• The angle of incidence (i) is equal to the angle of reflection (r).
Law of Refraction
The change in direction of a light ray depends on how the speed of light changes when it crosses
from one medium to another (Figure E). The speed of light is greater in medium 1 than in
medium 2 in the situations shown here. (a) A ray of light moves closer to the perpendicular
when it slows down. This is analogous to what happens when a lawn mower goes from a
footpath to grass. (b) A ray of light moves away from the perpendicular when it speeds up.
