The grade 11 CAPS geometrical optics presentation

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5. Geometrical optics
Physics
Grade 11

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Introduction
Geometrical optics is the study of how light interacts with materials and in particular with the
shapes of the materials and the angles at which light rays hit it.
Light rays are lines which are perpendicular to the light’s wavefronts. In geometrical optics
we represent light rays with arrows with straight lines.
Light rays reflect off surfaces. The
incident ray shines in on the surface and
the reflected ray is the one that bounces
off the surface. The normal is the line
perpendicular to the surface where the
light strikes the surface.
The angle of incidence is the angle
between the incident ray and the surface,
and the incident ray, reflected ray, and
the normal, all lie in the same plane.

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Law of reflection
The Law of reflection states the angle of incidence ( ) is equal to the angle of
reflection ( ) and that the reflected ray lies in the plane of incidence.
θi
θr

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Properties of light
Light can be reflected, refracted, absorbed or transmitted. Reflection and refraction are
covered in more detail elsewhere in this chapter.
Absorption of light is closely linked to reflection. Some wavelengths of light are reflected off
objects while others are absorbed by the object. This is what gives objects their colour.
Light can be transmitted through objects. Objects that allow the transmission of light are
called transparent and objects that do not are called opaque.
The last property of light that we will look at is the speed of light. Light also has a maximum
speed at which it can propagate, and nothing can move faster than the speed of light.
The speed of light, c, is constant in a given medium and has a maximum speed in vacuum
is
3×108
m⋅s−1

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Refraction
Refraction occurs at the boundary of two
media when light travels from one medium
into the other and its speed changes but its
frequency remains the same. If the light ray
hits the boundary at an angle which is not
perpendicular to or parallel to the surface,
then it will change direction and appear to
‘bend’.

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Refractive index and optical density
The refractive index (symbol n) of a material is the ratio of the speed of light in a vacuum to
its speed in the material and gives an indication of how difficult it is for light to get through
the material.
If the refractive index, n, increases, the speed of light in the material, v, must decrease.
Therefore light travels slower through materials of high refractive index, n.
Optical density is a measure of the refracting power of a medium.
n=
c
v

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Terminology
● The normal to a surface is the line which is perpendicular to the plane of the surface.
● The angle of incidence is the angle defined between the normal to a surface and the
incoming (incident) light ray.
● The angle of refraction is the angle defined between the normal to a surface and the
refracted light ray.

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Snell's law
Snell’s Law gives the relationship between the refractive indices, angles of incidence and
reflection of two media.
● Light travelling from one medium to another of lighter optical density will be refracted towards
the normal.
● Light travelling from one medium to another of lower optical density will be refracted away
from the normal.
n1 sin θ1=n2 sinθ2

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Critical angle
The critical angle is the angle of incidence where the angle of refraction is 90°. The light must
travel from an optically more dense medium to an optically less dense medium.
θc=sin−1
(n1
n2
)

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Total internal reflection
Total internal reflection takes place when light travels from one medium to another of lower
optical density. If the angle of incidence is greater than the critical angle for the medium,
the light will be reflected back into the medium. No refraction takes place.
Total internal reflection is used in optical fibres in telecommunication and in medicine in
endoscopes. Optical fibres transmit information much more quickly and accurately than
traditional methods.

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