Chapter 1

CHAPTER 1

GEOMETRICAL OPTICS

PHY250Geometrical OpticsBy: M.Najib Harif

1.1. Model of Light: Rays and Waves

There are two historical models for the nature of light. The speed of light has been measured in many ways. Before the beginning of the nineteenth century, light was considered to be a stream of particles. The particles were either emitted by the object being viewed or emanated from the eyes of the viewer.

Nature of Light – Alternative View

Christian Huygens argued that light might be some sort of a wave motion. Thomas Young (in 1801) provided the first clear demonstration of the wave nature of light.

He showed that light rays interfere with each other.

Such behavior could not be explained by particles.

Confirmation of Wave Nature

During the nineteenth century, other developments led to the general acceptance of the wave theory of light. Thomas Young provided evidence that light rays interfere with one another according to the principle of superposition.

This behavior could not be explained by a particle theory.

Maxwell asserted that light was a form of high-frequency electromagnetic wave. Hertz confirmed Maxwell’s predictions.

Ray model and wave modelWe can use rays to explain reflection and refraction of light.

Light waves spread out

Light rays travels in straight lines

Both the ray model and wave model can explain phenomena of light.

straight wavefronts parallel beam

• Beam = a set of rays

Light beam and light rays

Ray = straight line + arrow(indicating travelling direction)

convergent beams

parallel beams

divergent beams

Types of beams:

Ray Approximation

The rays are straight lines perpendicular to the wave fronts. With the ray approximation, we assume that a wave moving through a medium travels in a straight line in the direction of its rays.

1.2. Reflection

reflected rayincident ray

normal

mirror

angle of incidence

angle of reflection

Useful words to describe the reflection of light

normal

incident ray reflected ray

mirror

Laws of reflection

1. The incident ray, reflected ray and the normal all lie in the same plane.

normal


mirror

2. Angle of incidence = Angle of reflection

Laws of reflection

Specular Reflection

Specular reflection is reflection from a smooth surface.The reflected rays are parallel to each other.All reflection in this text is assumed to be specular.

Diffuse Reflection

Diffuse reflection is reflection from a rough surface.The reflected rays travel in a variety of directions.A surface behaves as a smooth surface as long as the surface variations are much smaller than the wavelength of the light.

Example

The angle between an incident ray and the mirror is 20.The angles of incidence and reflection are ____ and ____.

The mirror turns the ray by ____ .

20

(a) ‘ When hunting a fish under water, you should aim your spear directly at the fish.’

Do you agree?

Yes, of course.

No, because the fish is actually located somewhere else.

No, because size of objects changes when they are put under water.

1.3. Refraction of Light

(b) When sunlight falls on the water surface, which of the following occur(s)?

It is reflected back to the air.

It refracts into the water.

It is absorbed by water and turned into heat.

Refraction is the bending of light when the light passes from one medium to another.

air

glass

• Introduction

Useful words to describe refraction of light:

air

glass

normal

incident ray

angle of refraction

angle of incidence

refracted ray

• e.g. from air to glass

• Light is bent towards the normal.

air

glass

incident ray

normal

refracted ray

(a) From a less dense to a denser medium

(b) From a denser to a less dense medium

• e.g. from water to air

• Light is bent away from the normal.

refracted rayair

water

incident ray

normal

• Index of refraction

The index of refraction defines the velocity of light in the optically denser medium c /n.

v

cn

Speed of light in vacuum (air)

Speed of light in a medium (e.g. water)

Index of refraction

sin i is directly proportional to sin r.

• Relation between angle of incidence and angle of refraction

sin i

sin rO

i = angle of incidence

r = angle of refraction

straight line passing through the origin

incident ray

refracted ray

air

glassrefracted ray

normal

• The incident ray, the refracted ray and the normal all lie in the same plane.

Law of refraction

i.e. sin isin r

= constant

• The ratio of the sin i to sin r is constant.

This is called Snell’s law.

Law of refraction

In general,

n1 sin 1 = n2 sin 2n1 sin 1 = n2 sin 2

Material Refractive index

Glass 1.5 – 1.7

Water 1.33

Perspex 1.5

Diamond 2.42

Refractive indices of some materials

Frequency Between Media

As light travels from one medium to another, its frequency does not change.

oBoth the wave speed and the wavelength do change.

oThe wavefronts do not pile up, nor are they created or destroyed at the boundary, so ƒ must stay the same.

Index of Refraction ExtendedThe frequency stays the same as the wave travels from one medium to the other. v = ƒλ

ƒ1 = ƒ2 but v1 v2 so λ1 λ2

The ratio of the indices of refraction of the two media can be expressed as various ratios.

The index of refraction is inversely proportional to the wave speed.o As the wave speed decreases, the index of refraction

increases.o The higher the index of refraction, the more it slows downs the

light wave speed.

1 1 21

2 2 12

cλ v nn

cλ v nn

More About Index of Refraction

The previous relationship can be simplified to compare wavelengths and indices: λ1n1 = λ2n2

In air, n1 = 1 and the index of refraction of the material can be defined in terms of the wavelengths.

in vacuum

in a mediumn

λ λn

λ λ

Examples of refraction of light

(a) Bent chopstick

The chopstick appears bent because of refraction

(b) Shallower in water

The depth that the object is actually at is called the real depth (d).

O

Ireal depth

1

2'n

ndd

d’ = apparent depth

d = real depth

Light traveling in air strikes a flat piece of uniformly thick glass at an incident angle of 60°, as shown. If the index of refraction of the glass is 1.50, (a) what is the angle of refraction θA in the glass; (b) what is the angle θB at which the ray emerges from the glass?

Example 1

Solution:

Example 2

A searchlight on a yacht is being used at nightto illuminate a sunken chest as in figure. Atwhat angle of incidence, θi should the light be

aimed?

Solution:

Example 3Apparent depth of a pool

A swimmer has dropped her goggles to the bottom of a pool at the shallow end, marked as 1.0 m deep. But the goggles don’t look that deep. How deep do the goggles appear to be when you look straight down into the water?

Solution:

If light passes into a medium with a smaller index of refraction, the angle of refraction is larger. There is an angle of incidence for which the angle of refraction will be 90°; this is called the critical angle:


air

glassC C

refracted ray

sin 90o

sin Cn =

1 sin C n = C = sin1or 1

n( )

1.4. Total Internal Reflection

If the angle of incidence is larger than this, no transmission occurs. This is called total internal reflection.

Conditions for total internal reflection to occur are:Light must be refracted from a denser

medium to a less dense medium.The angle of incidence must be

greater than the critical angle, θi > θc

Example of total internal reflection

Mirage

Hurray!

On a hot day, you may see a pool of water at a distance in a desert.

Sorry! What you see is

just a MIRAGE.

It happens due to total internal reflections.

layers of air near the ground• hot• less dense than upper air• lower refractive indices

light refracted more and more towards the horizontal

When light meets a layer of air near the ground at an angle greater than C,

Total internal reflections occurs.

Image of the sky

For a given material, the index of refraction varies with the wavelength of the light passing through the material. This dependence of n on λ is called dispersion. Snell’s law indicates light of different wavelengths is bent at different angles when incident on a refracting material.

1.5. Dispersion