Electrons, waves and photons

All electromagnetic waves have the following properties in common:

• They are all transverse waves

• They can all travel in a vacuum

• They all travel at the same speed in a vacuum (free space) — the speed of light

What is speed of light?

Given in booklet

The speed of light in air is approximately the same as in a ______

vacuum

EM waves consist of ___________ ____ _____oscillating at ___ _____ to each other and to the direction in which the wave is travelling

electric and magnetic fields

right angles

all waves in this EM spectrum can (cuz they are transverse):

• Reflect

• Refract

• Diffract

• Be polarised

• Produce interference patterns

What is order of EM?

Radio waves

Microwaves

Infrared

Visible light

UV

X-ray

Gamma ray

How are EM waves arranged?

longest wavelength to shortest wavelength

Longer wavelength =

Lower E

Low frequency

Short wavelength=

Higher E

High frequency

EM waves diagram

Radio uses

• Communication (radio +tv)

Microwave uses

• Heat food

• Communication (wifi, mobile phones, satellites)

IR uses

• Remote controls

• Fibre optic communications

• Thermal imaging (medicine + industry)

• Night vision

• Heating/ cooking things

• Motion sensors

Visible light uses

• Seeing

• taking photos and videos

UV uses

• security markings (fluorescence)

• fluorescent bulbs

• getting a sun tan

X-ray uses

• X-ray images (medicine, industry and security at airports)

Gamma ray uses

• treating cancer

• sterilising medical equipment

aprox. wavelength range (m) of radio

>0.1

aprox. wavelength range (m) of micro

0.1- 1×10-³

aprox. wavelength range (m) of IR

1×10-³ - 7X10^-7

aprox. wavelength range (m) of visible

4×10^-7 - 7×10^-7

aprox. wavelength range (m) of UV

4×10^-7 - 1×10^-8

aprox. wavelength range (m) of X-rays

1×10^-8 - 4×10^-13

aprox. wavelength range (m) of gamma rays

1×10^-10 - 1×10^-16

from these values use _____ to work out range of frequencies

c = fλ where c is the speed of light:

Polarisation definition

Particle oscillations occur in only one of direction perpendicular to the direction of wave propagation

Polarisation can only occur in ______ waves

transverse

Why does polarisation can only occur in transverse waves

electromagnetic transverse waves are oscillating electric and magnetic fields in any plane perpendicular to the propagation direction

When transverse waves are polarised, this means:

• Vibrations are restricted to one direction

• These vibrations are still perpendicular to the direction of propagation / energy transfer

Longitudinal waves (e.g. sound waves) ______ be polarised and why

cannot

because they oscillate parallel to the direction of travel

polariser e.g.

polarising filter (light)

metal grilles (microwaves)

plane-polarised definition

only allows oscillations in a certain plane to be transmitted

why a metal grille is different from a polarising filter

• The free electrons moving in the metal bar can cancel out the electric field in the same direction as the grille and completely absorb it

• Thus the horizontal electric field passes if the grilles are positioned vertically and vice versa

The resulting graph of the light intensity with angle, as the second polariser is rotated through 360°

When does refraction occur?

Light passes a boundary between two different transparent media, where they change direction

Change in direction depends on which media the light rays pass between

• Air to glass (less dense to more dense): light bends towards the normal

• Glass to air (more dense to less dense): light bends away from the normal

• Along normal, light doesn’t bend at all

More dense= towards normal

Why does the change in direction occur in refraction?

Change in speed of wave when traveling in different substances (denser substance, rays slow down, hence bend towards the normal)

What changes during refraction?

Change: Speed and wavelength

Doesn’t change: frequency

What is refractive index?

Measure of how much light slows down when passing through it

What n= c/v mean + units

n= the index of refraction

c= speed of light in a vacuum (m/s)

v= speed of light in a substance (m/s)

What is a material with a high refractive index called and make light travel slower/faster?

Optically dense

Slower

What is the refractive index of light and why?

Aprox 1

Cuz light doesn’t slow down significantly when travelling through air as opposed to a vacuum

n will always be greater / less than 1

greater

snell’s law

relates the angle of incidence to angle of refraction (not given in equation sheet)

What symbols mean in snell’s law

n1= refractive index of material 1

n2= refractive index of material 2

θ1= angle of incidence of the ray in material 1

θ2= the angle of refraction of the ray in material 2

When the angle of refraction is exactly ___ the light is refracted along the boundary.

The angle of incidence is known as the _______

90°

critical angle C

Critical angle (given) can be found using and what can it be derived from

Sin(C)=1/n

• This can easily be derived from Snell’s law where:

  • θ₁ = C 

  • θ₂ = 90°

  • n₁  = n

  • n₂ = 1 (air)

Total internal reflection (TIR) occurs when:

angle of incidence is greater than the critical angle

the incident refractive index n₁ is greater than the refractive index of the material at the boundary n₂

two conditions for total internal reflection are:

• The angle of incidence, θ₁ > the critical angle, C

• Refractive index n₁ > refractive index n₂ (air)

How find and draw all the angles

Refraction definition

light travels at a different speed when travelling through another medium

Diffraction definition

spreading out of waves when they pass an obstruction

• This obstruction is typically a narrow slit known as an aperture

only property of a wave that changes when it diffracts is _____ and why

amplitude

because some energy is dissipated when a wave is diffracted through a gap

effects of diffraction are most prominent when _______

the gap size is approximately the same or smaller than the wavelength of the wave

_______ ______ of light can be represented as a series of light and dark fringes which show the areas of maximum and minimum intensity

diffraction pattern

If the laser were to be replaced by a non-laser source emitting white light

• The central maximum would be white

• All maxima would be composed of a spectrum

• The shortest wavelength (violet / blue) would appear nearest to the central maximum

• The longest wavelength (red) would appear furthest from the central maximum

• The fringe spacing would be smaller and the maxima would be wider

principle of superposition states:

When two or more waves with the same frequency arrived at a point, the resultant displacement is the sum of the displacements of each wave

Superposition in sound e.g.

stationary, longitudinal sound waves in a resonance tube such as in an organ pipe or woodwind instruments such as a flute

Superposition experiments with sound often use what?

air columns or speakers

If two loudspeakers are connected to the same signal generator, the superposition of the sound waves can be heard when walking along in front of the speakers

• A loud sound is heard when the sound waves _______

• A quiet or no sound is heard when the waves ________

• reinforce one another

• cancel each other out

The superposition of light waves is demonstrated through:

• Young's double-slit experiment

• Diffraction grating

in young’s double-slit experiment the light waves are _______ when they reach a screen

what does this show?

superposed

shows an interference pattern

___________ is commonly used for these experiment to produce the clearest interference pattern on the screen

Monochromatic laser light

distance between the maxima and minima on the pattern varies with the _____ of the light

frequency

interference of microwaves creates a ________ inside a microwave oven, which is used to heat food

standing wave

Microwave superposition experiments normally include:

• Two microwave transmitters

• A microwave detector

To produce a microwave stationary wave, a ______ is often used too, with just one transmitter

microwave reflector

Complete constructive or destructive interference is seen most clearly when the two superposing wave have the ________

same speed, frequency and amplitude

Graphical representation of superposition

How to find resultant of two waves

The best way to draw the superposition of two waves is to find where the superimposed wave has its maximum and minimum amplitude. It is then a case of joining them up to form the wave. Where the waves intersect determines how much constructive or destructive interference will occur.

When does interference occur?

when waves overlap and their resultant displacement is the sum of the displacement of each wave

When does constructive interference occur?

When two waves with the same frequency and amplitude arrive at a point in phase

The peaks and troughs line up on both waves and the resultant wave has double the amplitude

When does destructive interference occur?

When two waves with the same frequency and amplitude arrive at a point in anti-phase

The peaks on one wave line up with the troughs of the other. The resultant wave has no amplitude

Waves are said to be coherent if they have:

• The same frequency

• A constant phase difference

Coherence is vital in order to produce what?

an observable, or hearable, interference pattern

Path difference is defined as:

The difference in distance travelled by two waves from their sources to the point where they meet

Phase difference is defined as and given in what:

The difference in phase between two waves that arrive at the same point

degrees/ radians

Two waves with a path difference will also have a difference in _____

phase

Path difference is determined in ____

multiples of a wavelength

Constructive interference occurs when there is a path difference of __

nλ

Destructive interference occurs when there is a path difference of __

(n + ½)λ

phase difference between two waves is determined by ____

angle, in radians or degrees

Constructive interference occurs when ____

phase difference is an even multiple of π or that they are in phase

Destructive interference occurs when ______

phase difference is an odd multiple of π or that they are in anti-phase

When

In phase, causing constructive interference

what happens?

• The peaks and troughs line up on both waves

• The resultant wave has double the amplitude

When

In anti-phase, causing destructive interference

• The peaks on one wave line up with the troughs of the other

• The resultant wave has no amplitude

In two source interference of sound waves when does constructive and destructive interference occur?

• Constructive interference occurs when two compressions or two rarefactions line up and the sound appears louder

• Destructive interference occurs when a compression lines up with a rarefaction and vice versa. The sound is quieter

When can two source interference for microwaves be detected?

with a moveable microwave detector

When a two source interference of microwaves where does constructive and destructive interference occur?

• Constructive interference occurs in regions where the detector picks up a maximum amplitude of the signal

• Destructive interference occurs in regions where the detector picks up no signal

For two-source interference fringes to be observed, the sources of the wave must be:

• Coherent (constant phase difference)

• Monochromatic (single wavelength)

What is the path difference in Young’s double slit experiment

wave from slit S₂ has to travel slightly further than that from S₁ to reach the same point on the screen

• The difference in this distance is the path difference

• n is the order of the maxima/minima since there is usually more than one of these produced by the interference pattern

• n = 0 is taken from the middle, n = 1 is one either side and so on

What does Young’s double slit experiment show?

how light waves can produce an interference pattern

Set up of young’s double slit experiment

How does young’s double slit experiment work

• When a monochromatic light source is placed behind a single slit, the light is diffracted producing two light sources at the double slits A and B

• Since both light sources originate from the same primary source, they are coherent and will therefore create an observable interference pattern

• Both diffracted light from the double slits create an interference pattern made up of bright and dark fringes

Wave Theory of Light 

explains the phenomena of diffraction and refraction

• This theory describes light as a series of wavefronts on which every point is a source of waves that spread out and travel at the same speed as the source wave

• These are known as Huygens’ wavelets

Double slit equation: λ= ax/D

λ= wavelength of source (m)

a= distance between centres of the slit /separation of the two slits.

x= fringe width (distance between successive bright fringes) (m)

D= distance between double slit to the screen (m)

When the double slit equation only work?

a << D

THz to Hz

1×10^12

remember when calculating X if looks like

15×10^-3 ➗ 9

(➗ n. of wavelengths)