Light & Energy lessons

Waves and their properties

A wave is a repeating disturbance that carries energy from place to place. Light needs no material to travel through, so it can cross empty space.

The wavelength is the distance from one crest to the next. The amplitude is the height of a crest above the rest line.

A wave diagram that steps through wavelength, amplitude, and crests and troughs, marking each one.

The frequency is how many waves pass a point each second. It is measured in hertz (Hz), and 1 Hz means one wave per second.

Practice: Label the wave

Drag each wave term onto the picture that marks it.

Speed, frequency and wavelength

Each second a source sends out f waves, and each one is \lambda metres long. So the wave travels f \times \lambda metres every second.

Wave equation: v = f\lambda

A source sends out waves for one second; the count and the distance travelled give the speed.

Speed is in m/s, frequency in Hz and wavelength in metres. For light in empty space the speed is always c = 3.00 \times 10^8\ \text{m/s}.

Orange light has a frequency of 5.0 \times 10^{14}\ \text{Hz}. Rearrange the equation to find its wavelength.

1. \lambda = \frac{c}{f} (divide both sides by f)
2. \lambda = \frac{3.00 \times 10^8}{5.0 \times 10^{14}} (substitute)
3. \lambda = \textcolor{#f871b9}{6.0 \times 10^{-7}}\ \text{m} = \textcolor{#f871b9}{600}\ \text{nm} (1 nm is a billionth of a metre)

Practice: Use the wave equation

Find a wavelength or frequency from c = f lambda, with the unit shown beside the answer.

The electromagnetic spectrum

Light is one member of the electromagnetic spectrum. All of these waves travel at c in empty space, but their wavelengths are very different.

From longest wavelength to shortest, they are radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. A shorter wavelength means a higher frequency.

The seven bands step by one at a time, each with its wavelength range, frequency range, source and uses.

X-rays and gamma rays are ionising: they can knock electrons out of atoms and damage cells. Ultraviolet can damage skin too, so we limit how much we absorb.

Practice: Order the spectrum

Put bands of the spectrum in order by wavelength, frequency or photon energy.

Photons

Light energy arrives in tiny packets called photons. The energy of each photon depends only on its frequency.

Photon energy: E = hf

Here E is in joules and h = 6.63 \times 10^{-34}\ \text{J s} is the Planck constant. A photon of blue light, with f = 6.5 \times 10^{14}\ \text{Hz}, carries this much energy.

1. E = 6.63 \times 10^{-34} \times 6.5 \times 10^{14} (substitute h and f)
2. E = 4.31 \times 10^{-19}\ \text{J} (multiply the numbers, add the powers)

Two beams carry the same power; the bluer one sends fewer, bigger photons.

Brighter light means more photons each second, not bigger ones. Bluer light carries the same energy in fewer, bigger packets.

Practice: Photon energy

Work out a photon energy from its frequency or wavelength, in units of 10^-19 J.

Evidence for photons

Shine light on a clean metal and it can knock electrons out of the surface. This is the photoelectric effect.

Photons of a chosen colour and brightness hit a potassium plate; electrons only escape when each photon has enough energy.

Each electron is freed by one photon. Below a certain frequency nothing happens, however bright the light.

A smooth wave cannot explain this, but photons can. Only a photon with enough energy frees an electron, and brighter light just sends more photons.

Reflection

Reflection happens when light bounces off a surface. Angles are measured from the normal, a line at right angles to the surface.

A ray hits a mirror at a changing angle; the angle of incidence and angle of reflection are marked and always match.

Law of reflection: i = r

The angle of incidence always equals the angle of reflection. A rough surface scatters light in every direction, which is called diffuse reflection.

Practice: Aim the reflected ray

Turn the reflected ray to the right angle for a given incident ray.

Refraction

Refraction is the bending of light as it passes from one material into another. It happens because light changes speed.

Wavefronts cross from air into glass, slow down, bunch up and turn toward the normal.

The side of the wave that reaches the glass first slows down first, so the wave turns. Slowing down bends light toward the normal, and speeding up bends it away.

The refractive index n = \frac{c}{v} tells you how much a material slows light. Glass has n = 1.50, so light in glass moves at 2.00 \times 10^8\ \text{m/s}.

Snell's law

Snell's law tells you exactly how far a ray bends. Both angles are measured from the normal.

Snell's law: n_1 \sin\theta_1 = n_2 \sin\theta_2

Change the angle and the material; the refracted ray and the Snell's law working update live.

For example, light passes from air (n = 1.00) into glass (n = 1.50) at 30° to the normal.

1. 1.00 \times \sin 30° = 1.50 \times \sin\theta_2 (substitute)
2. \sin\theta_2 = \frac{0.500}{1.50} = 0.333 (divide by 1.50)
3. \theta_2 = \textcolor{#8b5cf6}{19.5°} (inverse sine on a calculator)

Practice: Apply Snell's law

Calculate the angle of refraction for a random pair of materials and angle.

Total internal reflection

Light leaving glass for air speeds up and bends away from the normal. At one angle, the critical angle, the ray skims along the surface.

A ray inside glass meets the surface at a growing angle; the escaping ray fades and past the critical angle all the light reflects.

Beyond the critical angle no light escapes. All of it reflects back inside, which is called total internal reflection.

For a material meeting air, \sin c = \frac{1}{n}. Optical fibres trap light this way to carry data for many kilometres.

Practice: Predict the ray

Pick the picture that shows what a ray does at a boundary.

Diffraction

Diffraction is the spreading of a wave as it passes through a gap or around an edge. It is strong evidence that light is a wave.

Waves pass through gaps of three widths; the narrowest gap spreads them the most.

The spreading is biggest when the gap is about the same size as the wavelength. Light has a tiny wavelength, so you only see it through very narrow slits.

Interference

When two waves meet, they add together. This is called superposition.

Two waves and their sum; shifting one wave moves the sum from double height to nothing.

Peaks that line up make a bigger wave, which is constructive interference. A peak meeting a trough cancels out, which is destructive interference.

Light through two narrow slits makes bright and dark bands on a screen. The bands are bright where the two paths differ by a whole number of wavelengths.

Practice: Constructive or destructive

Sort situations into constructive and destructive interference.

Energy transfer by radiation

Every object gives out thermal radiation, and at everyday temperatures it is mostly infrared. It needs no material to travel through, which is how the Sun heats the Earth across empty space.

The spectrum given out by objects from body temperature to the Sun, with the peak wavelength and power per square metre.

Hotter objects give out far more energy, and their peak moves to shorter wavelengths. That is why hot metal glows red, then yellow, then white.

Dark, matt surfaces are the best absorbers and emitters of radiation. Light, shiny surfaces reflect most of it instead.

Practice: Match the glow

Match each hot object to the wavelength where its radiation peaks.

Practice: Final review

Mixed questions from the whole course.