OCR A-Level Physics/Electrons, Waves and Photons NEW SPECIFICATION/Waves

Wave properties

A progressive wave is an oscillation that travels through space. All progressive waves transfer energy from one place to another.

Transverse and longitudinal waves

Transverse waves are waves where the oscillations of particles are perpendicular to the direction of travel of the wave. Longitudinal waves are waves where the oscillations of particles are parallel to the direction of travel.

Quantities to do with a wave

The displacement $s$ of a particle along a wave is the distance of the particle from the line of equilibrium or the line of zero displacement. The amplitude $A$ of a wave is the maximum displacement attained by particles along the wave during a cycle. The wavelength $\lambda$ of a wave is the distance between two adjacent points along a wave oscillating in phase. These quantities are measured in metres (m).

The period $T$ of a wave is the time taken for the wave to travel one wavelength. This is measured in seconds (s).

The frequency $f$ is the number of wavelengths passing a point per unit time. This is measured as the number per second (s^-1), which is equivalent to the alternative unit, the Hertz (Hz)

The wave speed $v$ is the distance travelled by a wave per unit time. This is measured in metres per second (ms^-1).

The wave speed equation

Frequency is related to the time period of a wave by the equation;

$f=\frac{1}{T}$

Speed is related to distance $d$ and time $t$ by the equation;

$v=\frac{\mathrm{\Delta }d}{\mathrm{\Delta }t}$

The wave moves a distance of one wavelength $\lambda$ in a time of one time period $T$, therefore;

$v=\frac{\lambda }{T}$

$v=(\frac{1}{T})\lambda$

$v=f\lambda$

The above is known as the wave speed equation which relates wave speed to frequency and period.

Phase difference

The phase difference $\varphi$ is the difference in phase between two oscillating particles. This is the difference between two particles in the fraction of an oscillation completed by the particles.

$\varphi =\frac{x}{\lambda }\times 2\pi$

Where $x$ is the separation between the two particles.

Processes affecting waves

Reflection

Diagram showing the reflection of light against a mirror

Reflection occurs when a wave changes direction at a boundary between two media but remains in the original medium. The angle made between the incident wave and the normal to the boundary at the point where the wave meets the boundary (angle of incidence ${\theta }_i$) is always equal to the angle made between the reflected wave and the normal (angle of reflection ${\theta }_r$).

Refraction

Refraction occurs when a wave changes speed and direction moving from one medium to another. The frequency of the wave stays constant. This means that the initial and final wavelengths and speeds are related in the following manner;

$\frac{v_1}{{\lambda }_1}=\frac{v_2}{{\lambda }_2}$

Diffraction

Diffraction is the spreading of a wave when passing through a narrow gap or around an obstacle. In order for this to occur, the width of the gap $W$ must be roughly equal to the wavelength $\lambda$ of the wave.

$W\approx \lambda$

When the width is much greater than the wavelength, there is little diffraction.

Polarisation

Polarisation is the process of making a wave become plane-polarised. A plane-polarised waves has oscillations in one plane only.

Polarising filters block out light not aligned in the desired plane. If a wave has a component parallel to the desired plane, the wave resulting from a polarising filter will have a lower intensity. If a wave is perpendicular to the desired plane, the polarising filter will block out 100% of the radiation and the resultant intensity will be equal to zero.

Intensity of a wave

The intensity of a wave $I$ is defined as the radiant power $P$ passing perpendicular to a surface per unit area $A$, represented symbolically as;

$I=\frac{P}{A}$

The inverse square law states that the intensity of a wave is directly proportional to the square of the separation between the surface and the source;

$I\propto \frac{1}{r^2}$

$I=\frac{P}{4\pi r^2}\because A=4\pi r^2$

Since intensity is a measure of power per unit area, it has the units Watts per square metre or Wm^-2.

Electromagnetic waves

The EM Spectrum

The Electromagnetic (EM) Spectrum records all the different types of waves, from radio waves (highest wavelength) to gamma waves (lowest wavelength).

The EM Spectrum

Type	Maximum wavelength $\lambda$ / m
Radio	$10^6$
Microwave	$10^{-1}$
Infrared	$10^{-3}$
Visible	$7\times 10^{-7}$
Ultraviolet	$4\times 10^{-7}$
X-ray	$10^{-8}$
Gamma	$10^{-13}$

Note that x-rays and gamma rays have an overlap between $\lambda =10^{-10}$ m and $\lambda =10^{-13}$ m.

Shared properties of EM waves

All electromagnetic waves;

• can travel through a vacuum
• travel at the speed of light in a vacuum, $c$, which is equal to $3\times 10^8$ ms^-1
• are transverse
• consist of oscillating and magnetic fields perpendicular to one another

Since the velocity of an electromagnetic wave is equal to the speed of light in a vacuum, the wave speed equation can be written as;

$c=f\lambda$

Refraction, reflection and refractive index

Different media have different refractive indices. The refractive indices of the media either side of a boundary determine whether a wave will reflect or refract at the boundary. The more optically dense a material is, the lower the speed the wave travels through it. The refractive index of a material $n$ is the ratio between the speed of light in a vacuum $c$ and the speed of light in that material $v$;

$n=\frac{c}{v}$

Light travels at speed $c$ in a vacuum, so the refractive index of a vacuum is equal to one. Air is not much more optically dense than a vacuum, so the refractive index of air is roughly equal to one. The $n$ value of glass is roughly 1.5.

Snell's Law

Diagram showing the angles and quantities involved in Snell's Law. Note: the term 'interface' is used for 'boundary'

Snell's Law relates the angle made between an incident wave and the normal to a boundary (angle of incidence) to the angle made between a refracted wave and the normal to the boundary (angle of refraction) by the following equation;

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$

Where $n_1$is the refractive index of the original medium, $n_2$ is the refractive index of the resultant medium, ${\theta }_1$ is the angle of incidence and ${\theta }_2$ is the angle of refraction.