**Coherent waves** are waves of the same type (e.g. electromagnetic waves) with the same frequency, wavelength and a constant phase difference.

**Monochromatic light** emitted by a laser is coherent and has a single wavelength. White light is made up of waves with a range of frequencies and different phase differences, therefore, white light is not coherent.

High-intensity lasers can damage your eyes. To prevent this, the following precautions should be followed:

- Never point the laser at people’s eyes and avoid pointing it at reflective surfaces
- Protective goggles can be worn
- A sign can be placed on the door to inform others that a laser is being used
- Filers can be used to reduce the intensity of light produced by the laser

### Path Difference

When the waves from two coherent sources reach a point, calculating the path difference can tell use whether destructive or constructive interference will take place.

If the distance between Source 1 and a point P is x and the distance between Source 2 and point P is x, the path difference = x – x = 0. If the path difference is equal to zero or a whole number of wavelengths, nλ, the two waves will have arrived in phase so constructive interference will take place.

If the path difference is an odd number of half wavelengths (n + 1/2) λ, the waves will arrive out of phase and destructive interference will take place.

### Young's Double Slit Experiment

Young’s Double Slit experiment provided evidence for the wave-particle duality of light.

Interference is a property of waves so by showing the interference of light, Young proved that light can behave like a wave.

By shining coherent, monochromatic light through a double slit, the light diffracts and an interference pattern is produced on the screen showing a series of bright and dark fringes. The bright fringes are caused by the constructive interference of waves arriving in phase as the path difference is equal to nλ. The dark fringes are caused by destructive interference as the path difference is equal to (n + 1/2) λ.

The bright central fringe is labelled n = 0 and the bright fringes going outwards from the central fringe are labelled n = 1, n = 2 and so on (symmetrical either side of the central fringe).

When using white light, the interference pattern observed will have a bright white central fringe followed by fringes with a spectrum from blue to red.

The following equation can be used to calculate the fringe spacing:

**w = λD/s**

w is the fringe spacing

λ is the wavelength of the light

D is the distance between the slits and the screen

s is the slit separation

A similar experiment can be done using sound waves or microwaves. A transmitter can produce waves that travel through a double slit which are then received by a receiver.

### Single Slit Diffraction

Waves travelling through a gap/slit spread out, this is diffraction. The closer the slit separation is to the wavelength of the wave travelling through it, the more diffraction will occur. As the wavelength of visible light is very small, using a narrower slit will result in more significant diffraction.

The spectrum produced by light diffracted through a single slit has a wide, bright central maximum (double the width of the other fringes) with the bright fringes decreasing in intensity as they get further from the central fringe. The width of the central maximum depends on the light λ and the slit separation.

Using the equation, W = λD/s:

- As the wavelength of light increases (λ), the fringe spacing increases so the central maximum becomes wider and subsequent maxima are further apart
- As the slit separation (s) increases, the fringe spacing decreases and so the central maximum becomes narrower
- As distance between slit and screen increases (D), fringe spacing increases so central maximum becomes wider but less intense as the light is spread over a larger area

We can also compare the patterns produced by red light and blue light for the same setup. As red light has a longer wavelength than blue light, the central maximum for red light will be wider than it is for blue light.

Using white light, a central bright, white maximum will be observed with less intense fringes showing a spectrum from blue to red.

### Diffraction Gratings

Diffraction gratings are made up of thousands of narrow slits arranged very close together.

- Applications of diffraction gratings:

**Deriving dsinθ = nλ**

### Refraction

When waves travel from one medium into another, the difference in optical density results in the wave travelling at a different speed. The change in speed causes a change in wavelength – if the wave enters the medium at an angle, it will appear to change direction. This is refraction.

If a wave travels perpendicular to the boundary (or along the normal) between the two mediums no refraction takes place (the wave will not change direction).

The refractive index of a material determines the change in speed:

**n = c / c _{s}**

n is the refractive index of the material/substance

c is the speed of light in a vacuum (3.00 x 10^{8} ms^{-1})

c_{s} is the speed of light in the substance

The refractive index of air is approximately 1

Snell’s Law can be used to calculate the angle of refraction:

**n _{1}sinθ_{1} = n_{2}sinθ_{2}**

n_{1} is the refractive index of medium 1

θ_{1} is the angle of incidence

n_{2} is the refractive index of medium 2

θ_{2} is the angle of refraction

The angle of incidence is the angle between the incident ray and the normal. The angle of refraction is the angle between the refracted ray and the normal.

If a ray is travelling from a less optically dense material e.g. air into a more optically dense material e.g. glass, the ray will bend towards the normal. This means the angle of incidence will be larger than the angle of refraction.

If a ray is travelling from a more optically dense medium into a less optically dense medium, the ray will bend away from the normal (the angle of refraction will be larger than the angle of incidence).

### Total Internal Reflection

TO BE CONTINUED

### Optical Fibres

TO BE CONTINUED