3.3.2 - Refraction, Diffraction & Interference

Refractive Index (n)

A measure of the relative speed of light in a material compared to in a vacuum (3 x 10^8 ms^-1)

Refraction

Light changing velocity when it travels across the boundary between two materials.

A more optically dense material (higher refractive index) causes it to slow down and bend towards the normal and vice versa.

What changes when a wave refracts?

Wave speed and wavelength change.

Frequency stays the same

Calculating Refractive Index

n = c (vacuum) / c (material) = λ (vacuum) / λ (material

Refractive index of air

Air is considered a vacuum as it doesn’t slow light down significantly so has a refractive index of one

Snell’s Law

n1 sinθ1 = n2 sinθ2

• n1 is the refractive index of material 1

• n2 is the refractive index of material 2

• θ1 is the angle of incidence of the ray in material 1

• θ2 is the angle of refraction of the ray in material 2

Total Internal Reflection

All light gets reflected off of a surface instead of passing through and being refracted.

TIR - Conditions

• Light has to be more from a more optically dense medium (higher n value) into a less optically dense medium (lower n value).

• Angle of Incidence > Critical angle

Critical Angle

The angle of incidence which causes light to travel alongside the boundary due to an angle of refraction = 90*

Critical Angle Formula

sinθ c = n2 / n1

where n1 > n2

Uses of TIR

TIR is used in optical fibres which carry information in the form of light signals.

How do optical fibres work?

A light pulse is sent down an optical fibre and is detected at the other end generating a signal.

Optical Fibre Structure

Flexible thin tube of plastic or glass.

Inner core is more optically dense and surrounded by cladding which is less optically dense

Function of cladding

• protects the core from damage

• prevents signal degradation through light escaping the core, which can cause information to be lost

Signal Degradation causes -

• Absorption

• Dispersion

Absorption

Parts of the signal’s energy is absorbed by the fibre reducing the overall amplitude of the signal - could cause a loss of information

Dispersion

Causes Pulse Broadening which is when the received signal is broader then the original transmitted signal - broadened signals can overlap which causes loss of information.

Types of dispersion

• Modal

• Material

Modal Dispersion - what is it?

Light rays enter fibre at different angles so take different paths hence they could take different amounts of time to travel along the fibre

Modal Dispersion - How to reduce it?

Make the core very narrow to reduce the possible path differences the light could have.Mater

Material Dispersion - what is it?

Light consisting of different wavelengths will travel at different speeds in a material

Material Dispersion - How to reduce it?

Use monochromatic light

Path difference

The difference in the distance travelled by two waves

Coherent Light Source

A light source where all light waves emitted have the same frequency and wavelength with a constant phase difference.

Monochromatic light

Light of a single wavelength

Young’s Double Slit Experiment purpose

To demonstrate the wave properties of light.

How to make a light source cohesive

• Place single slit before a double slit to make the light have a constant phase difference

• Use a filter to make the light monochromatic

What did young’s double slit experiment show?

A series of bright (maxima) and dark (minima) fringes - the central fringe is always a bright fringe.

The path difference for light from one slit is different from the other slight so light meets on the screen in different phases.

Bright Fringes - causes

Light meets in phase and interferes constructively which occures when the path difference is a whole number of wavelengths (nλ).

Dark Fringes - Causes

Light meets out of phase and interferes destructively which occurs when the path difference is a whole number and a half wavelengths ((n+½)λ).

Young’s double slit equation

sw = λD

where -

• s = slit separation (m)

• w = fringe separation (m)

• λ = wavelength (m)

• D = distance from screen (m)

slit separation is measured from the centre of one slit to the centre of the next

Diffraction

The spreading out of waves as they pass through or around a gap.

The greatest diffraction occurs when the gap is the same size as the wavelength - when the gap is smaller most waves get reflected.

Single Slit Diffraction Pattern

A bright(est) central fringe double the width of all the other fringes with alternating dark and bright fringes on either side.

Intensity of fringes decreases from central fringe,

Singe slit - changing slit width

Increasing slit width = less diffraction so central maxima is narrower and more intense

Single Slit - changing wavelength

Increasing the wavelet will increase how much light diffracts causing a thicker less intense central maxima

White light single slit

White light double slit

Diffraction Grating Pattern

More distinct dark and bright fringes.

The central fringe is called the zero order line and then the first order lines and then the second order lines etc.

What is a diffraction grating?

A slide containing many equally spaced slits.

d = 1/N

where -

• d = distance between the slits

• N = number of slits per metre

Diffraction Grating equation

d sinθ = nλ

where -

• d = distance between the slits

• θ = the angle between the zero order line and next order line

• n = the order

• λ = the wavelength

Diffraction Grating - changing wavelength