VIII Light, Electromagnetic Waves & Photons

Properties of Light

Reflection

Objects behind a mirror are the same distance from the mirror pane as the ones in front of the mirror. Light rays reflected by a mirror retain their angle.

$i = r$

Where $i$ is the angle of the incident ray, and $r$ is the angle of the reflected ray.

Refraction

Light rays change direction when they enter a transparent substance from air, or leave one into air.

Enters substance: light is bend towards the normal.

Leaves substance: light is bend away from the normal.

Each substance that allows light to pass through has a refractive index ($n$) that defines the ratio of the angles of the ray going in and the ray bend inside of the substance.

$n = \frac{\sin i}{\sin r}$

Also

$n = \frac{\text{speed of light in air}}{\text{speed of light in substance}}$

Light is slowed down when it passes through a substance!

$\vert$ The refractive index of a substance differs for each color (wavelength) of light

Newton's Theory of Light

Light, according to Newton, consists of small particles called corpuscles. The theory assumes that light moves faster through whater than through air.

Huygen's Theory of Light

According to Huygen light consists of waves. The theory assumes that the speed of light decreases in water.

Thomas Young's double slit experiment showed that Huygen had to have the right idea because sending light rays through small slits produces interference pattern (a known property of waves).

Interference Patterns

When waves meet they can reinforce or cancel each other.

Constructive Interference

Wave signals reinforce each other when a crest meets a crest.

Destructive Interference

Wave signales weaken or cancel each other when a crest meets a trough.

The Speed of Light

$c = 299792.458km/s$ (in a vacuum)

Electromagnetic Waves

Maxwell showed that light consists of vibrating electric and magnetic fields inducing each other in turns. He concluded that the spectrum of electromagnetic waves extends beyond the spectrum of visible light.

The Electromagnetic Spectrum

see Wikipedia for a table of spectra.

Wavelength

The distance from one crest to the next.

The symbol for wavelength is the greek lowercase letter lambda $\lambda$.

Frequency

The number of crest – trough cycles per second, measured in Hertz. Symbol $f$

Speed

The distance travelled per second by a wave crest. $v$

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

For electromagnetic radiation traveling through a vacuum (space):

$f = c/\lambda$

The Photoelectric Effect & Einstein's Photon Thoery of Light

Metals emit electrons when hit by electromagnetic waves with a frequency above a certain value. The threshold value depends on the type of metal.

This effect should occur with any kind of frequency according to Huygen's wave theory of light. However it is observed to occur only at frequency's above the metal's work function (the threshold frequency required for the effect to occur).

Einstein's photon theory of light resolves this discrepancy, according to which

• each photon is a packet of em-waves moving in one particular direction and not spreading
• the energy of a photon is proportional to the frequency of its waves

Therefore an electron at the surface of a metal is emitted when hit by a photon carrying energy equal to or greater than the work function of the metal.

$W = fh$

$W = \text{work function}$
$h = \text{planck constant}$