Wave Properties Refraction, diffraction and superposition.

Wave Properties

Refraction, diffraction and superposition

The mug trick!

Today’s lesson

• Refraction of light

The mug trick!

Refraction

When a wave changes speed (normally when entering another medium) it may refract (change direction)

Water waves

Water waves travel slower in shallow water

Sound waves

• Sound travels faster in warmer air

Light waves

Light slows down as it goes from air to glass/water

Snell’s law

There is a relationship between the speed of the wave in the two media and the angles of incidence and refraction

i

r

Ray, NOT wavefronts

Snell’s law

speed in substance 1 sinθ1

speed in substance 2 sinθ2

=

Snell’s law

In the case of light only, we usually define a quantity called the index of refraction for a given medium as

n = c = sinθ1/sinθ2

cm

where c is the speed of

light in a vacuum and cm is the speed of light in the medium

vacuum

c

cm

Snell’s law

Thus for two different media

sinθ1/sinθ2 = c1/c2 = n2/n1

Refraction – a few notes

The wavelength changes, the speed changes, but the frequency stays the same

Refraction – a few notes

When the wave enters at 90°, no change of direction takes place.

A practical!

ir

Data collection and processing

• Table of raw results with quantity, unit, uncertainty and an agreement between the uncertainty and precision of measurements

• Data correctly processed (including graphs and line of best fit

• Uncertainties correctly propagated (calculated) and error bars on graph (max/min line of best fit)

Conclusion and evaluation

• Compare result with actual result (referenced)

• Discussion of possible systemmatic errors

• Identification of weaknesses with relevant significance

• Improvements based on weaknesses

• No “waffly” terms!

Diffraction

• Ripple Tank Simulation

Diffraction

Waves spread as they pass an obstacle or through an opening

Diffraction

Diffraction is most when the opening or obstacle is similar in size to the wavelength of the wave

Diffraction patterns HL later!

Diffraction patterns HL

bθ

n = 1

n = 2

bsinθ = nλ

θ = λ/b (radians)

Diffraction

Diffraction is most when the opening or obstacle is similar in size to the wavelength of the wave

Diffraction

That’s why we can hear people around a wall but not see them!

Diffraction of radio waves

Superposition

Principle of superposition

When two or more waves meet, the resultant displacement is the sum of the individual displacements

Constructive and destructive interference

When two waves of the same frequency superimpose, we can get constructive interference or destructive interference.

+ = + =

Superposition

In general, the displacements of two (or more) waves can be added to produce a resultant wave. (Note, displacements can be negative)

1. Constructive Interference - when the crests (or troughs) of two waves coincide, they combine to create an amplified wave.

The two waves are in phase with each other – there is zero phase difference between them.

2. Destructive Interference - where the crests of one wave are aligned with the troughs of another, they cancel each other out.

The waves are out of phase (or in antiphase) with each other – they are half a cycle different from each other.

Superposition

Let’s try adding some waves!

• Standing waves store energy, whereas travelling waves transfer energy from 1 point to another

• The amplitude of standing waves varies from 0 at the nodes to a max at the antinodes, but the same amplitude for all the oscillations along the progressive wave is constant.

• The oscillations are all in phase between nodes, but the phase varies continuously along a travelling wave.

Interference patterns

• Ripple Tank Simulation

If we pass a wave through a pair of slits, an interference pattern is produced

Path difference

Whether there is constructive or destructive interference observed at a particular point depends on the path difference of the two waves

Constructive interference if path difference is a whole number of wavelengths

Constructive interference if path difference is a whole number of wavelengths

antinode

Destructive interference if path difference is a half number of wavelengths

Destructive interference if path difference is a half number of wavelengths

node