Electromagnetic waves (4.4.2)

The full range of electromagnetic (EM) waves is collectively referred to as the electromagnetic spectrum.

Humans can only see visible light, but there are many other types of EM waves, including radio waves, microwaves, infrared radiation, ultraviolet radiation, X-rays, and gamma rays.

• Radio waves: Longest wavelength, lowest frequency. Applications: long-distance communication, radar, TV and radio broadcasting, wifi, and mobile phones.
• Microwaves: Shorter wavelength than radio waves. Applications: microwave ovens, Global Positioning System (GPS), satellite TV, and Doppler radar.
• Infrared (IR): Detected as heat; invisible to the eye. Applications: remote controls, night vision cameras, thermal imaging, motion sensors, and weather satellites.
• Visible light: Narrow range visible to humans; ROYGBIV (red to violet). Applications: photography, lighting, lasers, and fibre optics.
• Ultraviolet (UV): Shorter wavelength than visible light; invisible to the eye. Applications: fluorescent lights, sterilising equipment, and security features in banknotes.
• X-rays: Very short wavelengths; penetrate most materials. Applications: medical imaging (X-rays), and airport security scans.
• Gamma rays: Shortest wavelength, highest frequency and energy. Applications: radiotherapy, sterilising equipment, and gamma-ray telescopes.

From longest wavelength (lowest frequency) to shortest wavelength (highest frequency), the electromagnetic spectrum is comprised of:

All EM waves share similar properties:

• Transverse waves: The vibrations of the wave (the electric and magnetic fields) occur perpendicular to the wave’s direction of travel.
• Travel in vacuum: Unlike sound waves (which require a medium such as air or water), EM waves can travel through the emptiness of space.

• Speed in vacuum: All EM waves travel at the speed of light in a vacuum. It is the fastest possible speed.
• Speed in air: The speed of EM waves is slightly slower in air than in a vacuum, but for most purposes it is still considered to be
• In denser materials (e.g. water, glass), the speed of EM waves decreases due to interaction with the material’s particles.

An electromagnetic wave consists of two parts:

• an electric field
• a magnetic field

These fields are perpendicular (at angles) to each other and to the wave motion.

For a propagating wave, the electric field might oscillate vertically and the magnetic field horizontally. They oscillate in any direction perpendicular to each other.

EM waves all exhibit the same wave behaviours, such as reflection. This is when EM waves hit a boundary, causing them to bounce back.

Examples: light reflecting off a mirror and radio waves bouncing off the ionosphere for long-distance communication.

EM waves all exhibit the same wave behaviours, such as refraction. This is when EM waves pass into a new medium (e.g. air to water), causing their speed and direction change.

Example: Light bending through a glass prism.

EM waves all exhibit the same wave behaviours, such as diffraction. This is when waves pass through a small gap or around obstacles, causing them to spread out.

Example: Radio waves diffracting around buildings.

EM waves all exhibit the same wave behaviours, such as polarisation. This is when EM waves are filtered so their vibrations align in one direction.

Example: Sunglasses that reduce glare by blocking horizontal light waves

EM waves all exhibit the same wave behaviours, such as interference. This is when two waves overlap, they combine with either constructive interference, when the waves add up to create a stronger wave, or destructive interference, where the waves cancel out.

Example: Interference patterns in light waves, seen in double-slit experiments.

You need to memorise the approximate wavelength ranges for each type of EM wave.

Radio waves have wavelengths of and longer, whereas high energy gamma rays have wavelengths as short as , which is an order of magnitude shorter than the size of atomic nuclei!

You do not need to memorise both the frequency and wavelength ranges as all EM waves travel at the same speed in a vacuum so the wave equation can be used to convert from wavelength to frequency.

The wave equation is:

where:

• is the speed of light in a vacuum
• is the frequency in Hz
• is the wavelength in metres.

Polarisation is a process by which the vibrations of a transverse wave are restricted to a single direction.

The polarisation direction is always perpendicular to the direction of wave propagation.

Only transverse waves can be polarised because their vibrations naturally occur in directions perpendicular to their travel.

Longitudinal waves cannot be polarised as their vibrations occur in the same direction as the wave travels, and so the vibrations are already restricted to one direction.

Unpolarised waves:

• Vibrations occur in all possible planes perpendicular to the wave’s travel direction.
• Example: Light from natural sources such as the Sun, bulbs, and flames is unpolarised.
• Visualisation: Imagine a rope being shaken randomly in all directions – the wave has no fixed plane of oscillation.

Polarised waves:

• Vibrations are confined to a single plane perpendicular to the wave’s travel.
• Waves may be polarised in any direction, but the most commonly discussed are vertically and horizontally polarised waves:
  • In vertically polarised waves, particles are displaced in the vertical direction.
  • In horizontally polarised waves, particles are displaced in the horizontal direction
• Visualisation: Imagine a rope being shaken up and down in a single fixed direction.
• Even when polarised, the vibrations remain perpendicular to the wave’s travel direction.

Polarising filters are used to polarise light waves by only allowing vibrations in a specific direction to pass through.

A polarising filter has a transmission axis aligned in a specific direction. It blocks all vibrations except those parallel to its transmission axis. For example, sunglasses with polarising lenses reduce glare by filtering out certain planes of reflected light.

Parallel filters: When two filters are aligned with their transmission axes in the same direction, maximum light passes through.

Perpendicular filters: When two filters are aligned at to each other, no light passes through.

Polarisation can occur naturally when light interacts with matter.

• Scattering: As seen in the diagram above, light scattering in the atmosphere creates polarisation – the blue light from the sky is polarised more when the sun approaches the horizon.
• Reflection: Light reflecting off shiny surfaces, such as water or glass, becomes partially polarised, which causes glare.
• Refraction: Polarisation can occur when light bends while entering a medium at a specific angle.

When microwaves pass through a metal grille, the electric field component aligned with the grille is blocked due to the motion of the free electrons in the metal bars. The electric field component that is perpendicular to the grille passes through.

The direction of polarisation for microwaves is defined as the direction of the electric field perpendicular to the grille bars. For light, it is parallel to the filter’s axis.

Radio and television signals are broadcast with either horizontal or vertical polarisation.

To receive the broadcast signal effectively, the receiving aerial (antenna) must be aligned to match the polarisation of the transmitted wave.

• For horizontally polarised signals, the aerial should be mounted flat (horizontal).
• For vertically polarised signals, the aerial should be mounted upright (vertical).

Refraction occurs when light passes from one medium to another with a different refractive index, such as from air to glass or from glass to water. This change in medium causes a change in the speed of light, which in turn alters its direction.

The direction of refracted light is measured relative to an imaginary line known as the normal, which is drawn perpendicular to the surface of the boundary where the light ray enters or exits.

The angle formed between the light ray and the normal before refraction is called the angle of incidence, while the angle after refraction is called the angle of refraction.

Refraction at a boundary depends on the refractive indices on either side:

• When light moves from a lower refractive index medium to a higher one, it slows down and bends towards the normal.
• When light moves from a higher refractive index medium to a lower one, it speeds up and bends away from the normal.
• If light travels directly along the normal line, no bending occurs because the light remains perpendicular to the boundary.

Only the speed and wavelength of light change during refraction. The frequency remains constant. This is a consequence of energy conservation.

Snell’s law is a mathematical relationship that describes how light refracts when it crosses the boundary between two media. It relates the angles of incidence and refraction to the refractive indices of the two media:

where:

• and are the refractive indices of the first and second media, respectively
• and are the angles of incidence and refraction, measured from the normal.

The first medium, where the light originates, is referred to as material 1, while the second medium, where the light enters, is referred to as material 2.

The angles in Snell’s law must always be measured relative to the normal.

Note that if a question gives an angle relative to the surface of the boundary, you will need to subtract it from to calculate the correct angle relative to the normal.

The refractive index of a transparent semi-circular block can be calculated by measuring the light passing through the block at various angles of incidence.

A semi-circular block is used because light passing through the curved surface always hits the boundary at normal incidence, so it does not refract. Therefore, if light is shone on the flat surface, the angle at which the light leaves the block can be measured to determine the angle of refraction from the flat surface.

Variables in this experiment:

• Independent variable: The angle of incidence . This is the angle at which the light ray strikes the flat surface of the semi-circular block.
• Dependent variable: The angle of refraction . This is the angle at which the light ray exits the block relative to the normal.

Experimental method:

1. Setting up the apparatus: Place the semi-circular block on a protractor such that its flat side lies along the line.
2. Defining the normal line: Direct the light ray from the lightbox or laser toward the flat edge of the block at . Using a ruler and pencil, draw a dotted line perpendicular to this edge to represent the normal.
3. Tracing the light rays: Direct the light ray into the block at various angles of incidence, starting from and increasing in increments up to . For each angle, trace the path of the ray entering the block and the ray exiting the block.
4. Measuring refraction: After tracing the light rays, remove the block to measure the angles of incidence and refraction relative to the normal using the protractor. Record these values in a table.
5. Repeating for accuracy: Perform multiple trials for each angle to calculate averages, reducing random errors.

From measurements of the angle of incidence and angle of refraction , the refractive index can be calculated using Snell’s law, which can be written as:

If we are dealing with a material surrounded by air, then represents the refractive index of air, which is approximately 1, and the equation simplifies to:

To accurately determine the refractive index, plot a graph of (Y axis) against (X axis). The gradient of this graph is equal to the refractive index of the block.

Several errors and uncertainties may affect the accuracy of the results.

Systematic errors:

• Ensure that the block of material that is being measured is positioned correctly. Misalignment can lead to consistent errors in the measurements of angles.

Random errors:

• Use a sharp pencil to draw lines accurately, reducing uncertainty in the measured angles.
• The light from the lightbox may appear slightly blurry or dispersed, making it difficult to trace the ray accurately. A concentrated laser beam produces sharper rays, reducing this uncertainty.

When light travels from a medium with a high refractive index to one with a lower refractive index, such as from glass to air, it refracts away from the normal.

As the angle of incidence increases, the angle of refraction also increases.

Eventually, as the angle of refraction increases, the refracted ray travels exactly along the boundary between the two media. This specific angle of incidence is known as the critical angle, denoted by

At the critical angle, the angle of refraction is

If the angle of incidence is greater than the critical angle, light no longer refracts into the second medium. Instead, it is completely reflected back into the denser medium. This phenomenon is called total internal reflection.

Total internal reflection has numerous practical applications: