In this lecture the following are introduced:
• Early ideas
• Reflection
• Refraction (Snell's law)
• The wave nature of light
• Two slit interference
• Mirages and optical illusions

Early ideas about light

In the fifth century BCE, a Greek philosopher named Empedocles was impressed by the way cats' eyes shone in the dark. He proposed that light was something that flowed out from the eye. When objects came within the flow of the eye's light they caused a sensation of sight, rather like the way visually impaired people use a white cane to perceive objects in front of them as they walk. The distance to an object was estimated by how far the beam extended from the eye.

Others (like Archimedes and Pythagoras) thought this couldn't be true because you could see from near to far, instantaneously! They believed that luminous sources sent out light particles and that you had the sensation of "seeing" when these particles entered the eye.

For example: Lucretius 100BCE:
"And thus I say that portraits of objects -
tenuous shapes - are sent from off the object,
From off the utmost outside of the object,
Which are like films, or may be named a 'rind',
Because the image bears the same look and form
With whatever body has shed it fluttering forth."

They deduced that light usually travelled in straight lines. This was because you can see through a series of holes when they are lined up, but not when they are out of alignment. Also, shadows produced a likeness of the object.

They also knew that light changed direction when it entered a transparent medium because a spear appeared to be bent when a part of it was under water.

The Seventeeth Century

Robert Hooke proposed a wave theory of light in 1672 when he found that light bent around corners (diffraction).

In 1678 Christiaan Huygens's wavelet principle for new wavefront formation was published. He said that an expanding wavefront behaves as if each point on the wave front were a new source of waves with the same frequency and phase.

Isaac Newton didn't agree with wave theories. He said that light was made of particles (or "corpuscules"), which radiated at very high speeds from light sources. Each color corresponded with a certain type of particle. White light had all the different kinds of particles.

Reflection

This was explained by Newton as the particles bouncing, like balls bounce off a wall.

• The angle of incidence equals the angle of reflection.
• The incident angle, the normal and the reflected angle are all in the same plane.

Refraction

Refraction (or bending) occurs when light travels from air into glass, and was explained by Newton as the particles speeding up on entering the more dense glass (like sound does). The bent path is a minimum time path.

The angles are related by the refractive index, where
•The refractive index is the sine of the incident angle divided by the sine of the refracted angle.
•The incident angle, the normal and the refracted angle are all in the same plane.
•As Snell's law this is written:
A refractive index greater than 1 means the refracted ray bends towards the normal.
A refractive index less than 1 means the refracted ray bends away from the normal.

Example
A light ray is incident on a plane slab of glass (refractive index 1.5) at 60⁰ to the surface. Find the angle of refraction.

Andrea Mameli's Computer demonstrations

Christiaan Huygens

Huygens' explanation of reflection and refraction was by generating wavefronts from wavelets. Each point on a wavefront emits wavelets and the next wavefront is the envelope that forms after one period.

Huygen's construction for reflection

Huygen's construction for refraction

When a point on a wavefront coincides with the interface, then it emits a wavelet into the new medium at a different speed. After one period there will be a distance, d, along the interface where the wavefront in the first medium just reaches the interface. The wavefronts in the second medium will now be at a different angle from those in the first medium. The angle between the wavefront in the first medium and the interface is the incident angle, i.e. the same as the angle between the incident ray and the normal.
By geometry:

Here n₁₂ is called the relative refractive index from medium 1 to medium 2 and:

The speed of light in a vacuum (written below as "c") is always constant at 3 x 10⁸ m.s^-1.
The absolute refractive index of medium 1 is defined as the relative refractive index from vacuum to medium 1, so:

In terms of absolute refractive indices:

Example
A parallel sided slab of glass (n_g = 1.5) forms the wall of an aquarium so that it has air (n_a = 1.0) on one side and water (n_w = 1.3) on the other. A ray of light is incident at 250 to the glass, find the refracted angle in the glass and the emergent angle in the water.

Since the sides of the glass are parallel the incident angle from glass to water is the same as the refracted angle λ₂ in the glass.

Huygen's predicted that the speed of light slowed down when it enters a more dense medium. This was a direct contradiction of Newton, and so Huygen's idea was rejected on the basis of Newton's authority till the early 1800s.

Thomas Young

Thomas Young lived 1773-1829. He was an English physicist, physician, and Egyptologist.
• He described the modern concept of energy.
• He proposed a theory of color vision, and described astigmatism (a vision problem).
• He established a coefficient of elasticity (Young's modulus).
• He helped to decipher the Rosetta stone by recognising Pharaohs' names spelt as characters in cartouches (Champollion advanced from there).
• He argued for a wave theory of light.

In order to get his wave theory of light accepted, he had to argue that Newton had actually supported a wave theory. He pointed to the phenomena of the dark rings which appear when a shallow lens is placed on a flat glass surface.

As these were called "Newton's rings", he said Newton must have accepted wave-like phenomenon with light. Thus using Newton's authority, Young's theory was accepted.

Young's Two Slit Interference Experiment

When two sources emit waves that are in step with each other, i.e. the sources produce waves with a constant phase relationship, then the waves produce stationary patterns of constructive and destructive interference.

Here is an example with water waves

Notice that the sources emit waves at the same time and with the same period. When this happens the sources are said to be coherent.

Incoherent sources emit waves with different wavelengths, and/or emit waves with random phase differences.

A computer demonstration is given at: www.colorado.edu/physics/2000/schroedinger/two-slit2.html

Fringes appear because there are phase differences between the waves meeting at P. The phase differences are in turn produced by the different distances of the slits from P.

When PS₁ = PQ, then S₂Q is difference between the path lengths that the two waves travel.

This means:

When the phase difference is zero or a multiple of 2π, the waves reinforce and produce a maximum in the light's intensity (brightness).

bright fringe phase conditions

For bright fringes to appear, the phase difference between waves arriving at a point has to be an even number of π radians.
This is written mathematically as: φ = 2mπ where m = 0,+1,-1,+2,-2, etc

dark fringe phase conditions

For dark fringes to appear, the phase difference between waves arriving at a point has to be an odd number of π radians.
This is written mathematically as: φ = (2m + 1)π where m = 0,+1,-1,+2,-2, etc

Fringe conditions in terms of path differences:
When S₂Q is one wavelength, the distance, y, is the distance from the centre of the pattern to the first fringe, and so from similar triangles:

Bright fringes also appear up the screen for path differences which are whole multiples of the wavelength. These will be at distances from the centre given by:

where m = 0,1,2,3 …

The wavelength of the light can be measured from the fringe spacing, the slit separation and the distance between the slits and the screen.

Example
A double slit experiment has slits which are 5mm apart and on a screen which is 1.5m away the fringes are 0.16mm apart. Find the wavelength of the light.

The Visible Spectrum

Different wavelengths are seen by the eye as different colours. The normal human range is shown.

The visible spectrum thus ranges from about 400nm to 700nm, but this varies with individuals and age.

Mirages

Mirages are multiple images formed by atmospheric refraction. There are inferior and superior mirages. In an inferior (or "hot road") mirage there is an inverted image below the object caused by layer of hot air near the surface.

In an superior mirage there is an inverted image above the object caused by a layer of hot air above the surface.

The talking head is a mirage of a diferent kind.

Optical Illusions

Illusions cannot be photgraphed because they are a product of human perception. There are alternate perceptions in each of the following.
(1) face or liar                          (2) face or lovers kissing                                   (3) beauty or hag.
   

Summarising:

Light travels in straight lines. Newtons "corpuscular" theory explained reflection and refraction.
Snell's law defines refractive index:

Huygen's construction: each point on a wavefront emits wavelets and the next wavefront is the envelope that forms after one period.
Huygen also explained reflection and refraction and said that light slowed down in higher refractive media.
The relative refractive index is given by
The speed of light in a vacuum (written below as "c") is always constant at 3 x 10⁸ m.s^-1.
The absolute refractive index is given by
In terms of absolute refractive indices, Snell's law is:

Young's two slit experiment confirmed a wave nature for light.
When the phase difference between waves arriving from each slit is zero or a multiple of 2π, the waves reinforce and produce a maximum in the light's intensity (brightness).
Bright fringes appear up the screen, at distances from the centre given by: where m = 0,1,2,3 …

Mirages are caused by refraction (or reflection) and optical illusions are a product of human perception.