1. 4.3 Wave characteristics

2. A reminder - Wave fronts
Wave fronts highlight the part of a wave that is moving together (in phase).
= wavefront
Ripples formed by a stone falling in water

3. Rays
Rays highlight the direction of energy transfer.

4. Wave intensity

5. Wave intensity
This is defined as the amount of energy per unit time flowing through unit area
It is normally measured in W.m-2
I usually make a “square metre” using metre rulers to show this – this is then useful when talking about intensity and how it changes with distance from the source.

6. Wave intensity
For example, imagine a window with an area of 1m2. If one joule of light energy flows through that window every second we say the light intensity is 1 W.m-2.

7. Intensity at a distance from a light source
Can you follow Mr Porter please?
I normally go outside with some metres rulers taped into a 1 m2 square shape and discuss how much light from the sun goes through the 1 m2 and how we can calculate it.

8. Intensity at a distance from a light source
I = P/4πd2 where d is the distance from the light source (in m) and P is the power of the light source(in W)

9. Intensity at a distance from a light source
I = P/4πd2 d

10. Data booklet
I α x-2

11. Intensity and amplitude

12. Intensity and amplitude
The intensity of a wave is proportional to the square of its amplitude
I α A2
(or I = kA2)

13. Intensity and amplitude
This means if you double the amplitude of a wave, its intensity quadruples!
I = kA2
If amplitude = 2A,
new intensity = k(2A)2
new intensity = 4kA2

14. Surfers know this!

15. 4.3 Wave Intensity video

16. 4.3 Wave Intensity worksheet

17. Superposition

18. Principle of superposition
When two or more waves meet, the resultant displacement is the sum of the individual displacements

19. Constructive and destructive interference
When two waves of the same frequency superimpose, we can get constructive interference or destructive interference. + = = +

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

22. 4.3 Superposition Let’s try adding some waves!
Students can add togther the 2 waves by adding displacements along the waves to find the (strangely shaped!) resultant!

23. Polarized waves (transverse only)
Vibrations lie in the same plane

24. Polarized light
I usually demonstrate with a rope.

25. Polarized light 50% goes through (important)
Often a plastic called “Polaroid” discovered by a 19 year-old Harvard undergradutae called Edwin Land in 1928
Polarized light
They need to know that the intensity of unpolarised light transmitted is 50%.
50% goes through (important)

26. Polarized light
If you have polaroid filters they can play around to see this – no light transmitted by filters at 90° to each other.

27. Find a suitable place to look at a reflection in a window
Find a suitable place to look at a reflection in a window. The look through rotating polaroids – the reflection disappears showing polarisation by reflection!

28. Polarization by reflection

29. Brewster angle
In 1812, Sir David Brewster found experimentally that the reflected ray is 100% polarized when the angle between the reflected ray and the refracted ray is 90°

30. Brewster’s angle tanθB = n2/n1
If ray is incident from air, n1 = 1, so tanθB = n2
Completely polarized reflected ray
normal θB
You don’t need to know or use this formula!
η = n1
η = n2
They don’t need to know this. This is added just for interest.

31. Calculate Brewster’s angle for light incident on water (η = 1.33)

32. Calculate Brewster’s angle for light incident on water (η = 1.33)
tanθB = n2/n1 = 1.33/1 = 1.33
θB = 53.1º
You don’t need to know or use this formula!

33. Polarisation by dispersion!

34. Polarizers and analysers
A polarizer (like polaroid) can be used to polarize light

35. Polarizers and analysers
Another polarizer can also be used to determine if light is polarized. It is then called an analyser.

36. Malus’ Law
The intensity of polarised light that passes through a polarizer is proportional to the square of the cosine of the angle between the electric field of the polarized light and the angle of the polarizer!

37. Malus’ law
I = Iocos2θ Io
Iocos2θ

38. Optical activity
Some substances can change the plane of polarized light. We say they are optically active

39. Optical activity
Sugar solution is optically active. The amount of rotation of the plane of polarization depends on the concentration of the solution.

40. Stress analysis
Some substances, not normally optically active, become optically active if subject to stresses.

41. Stress analysis
Analysis of the patterns reveals how the stress varies in the material.

42. 4.3 Polarisation worksheet