1. Light & Waves L2 NCEA Achievement Standard 2.3
Text Book reference: Chapters 12,13 &14

2. Why Waves?
A wave is a method of transferring energy from one place to another without having to move any matter.
Examples of everyday waves include: water, light, sound, seismic waves.
They come in two forms: Transverse and Longitudinal

3. Transverse Waves
The particles that make up the wave vibrate at right angles to the direction of wave propagation.
Example: Light
Particle Motion
Direction of Wave Propagation

4. Longitudinal Waves
The particles that make up the wave vibrate back and forth in the same direction as the direction of wave propagation.
Example: Sound
Direction Of Wave Propagation
Particle Motion

5. Wave Terms
Amplitude - The distance from the undisturbed position of the particle to it’s maximum displacement
Symbol: A
Measured in metres
Amplitude

6. Wave Terms
Wavelength - The distance from one point on a wave to where it begins to repeat itself.
Symbol: l (Greek letter “lam-da”)
Measured in metres
Wavelength

7. Wave Terms
Period - the time it takes one wavelength to pass a given point
Symbol: T
Measured in seconds
Wave speed - the speed of wave propagation
Symbol: v
Measured in ms-1

8. Wave Terms Note: Frequency and Period are inverses of each other
ie. f =1/T or T = 1/f
Frequency - the number of waves that pass a given point per second
Symbol : f
Measured in Hertz Hz (or cycles per second s-1)

9. Wave Terms
Area of Compression- part of a longitudinal wave where the particles are squashed up
Area of Rarefaction- part of a longitudinal wave where the particles are spread out
Compression
Rarefaction

10. Wave Terms The top or peak of a transverse wave is called a crest
The bottom or dip of a transverse wave is called a trough
Crest
Trough

11. Wave Terms
Waves generated from a point source travel outwards in concentric circles called wavefronts.
A line in the direction of propagation is called a ray.
Wavefronts
Ray S

12. Wave Equation
This is the equation that relates wave speed, frequency and wavelength.
“c” is sometimes substituted for “v” when the wave is light.

13. Reflection & Transmission of Pulses
When a pulse moves from one medium into another, some of the pulse is reflected and some is transmitted.
Light to Heavy String
Heavy to Light String
Pg 224 Questions 14A 1-6

14. Reflection
Waves will bounce (reflect) off a flat surface at the same angle at which they hit it
A line at right angles to the surface is called the normal
Normal

15. Curved Reflectors
Convex Reflectors – make the waves diverge (spread out)

16. Curved Reflectors
Concave reflectors – make the wave converge (meet at a point)

17. Refraction
The bending of a wave as it goes from one medium into another.
When a wave travels from one medium into another it’s speed alters.
If the wave hits the boundary at an angle, one side will change speed before the other, skewing the wave around and changing it’s direction of propagation.

18. Refraction
Because the frequency of the wave is determined by the source, if the wave slows down, it’s wavelength must decrease. (And vice versa)
Fast Medium
Slow Medium

19. Angles in refraction
The angle between the incident (incoming) ray and the normal is called the angle of incidence
The angle between the refracted ray and the normal is called the angle of refraction.
Angle of Incidence
Angle of Refraction

20. Refractive Index
How much a wave is bent depends on the refractive indices of the two media.
Relative refractive index(2n1)is a ratio of the speeds of the waves in the two media
Absolute refractive index (n1or n2)is a measure of how much the speed is slowed when entering a medium from air ( or vacuum)

21. Snell’s Law Where: n= refractive index
q= angle of incidence/refraction
v= wave speed
l= wavelength
Medium 1 is the one the wave is leaving.
Medium 2 is the one it is entering.

22. Diffraction The bending of waves as they travel through gaps…..
The smaller the gap, the more the diffraction

23. Diffraction
….or around edges.
Pg 229 Questions 14B 1-6

24. Interference When two waves meet at one point they interfere.
Constructive interference is where a crest meets a crest, or a trough meets a trough.
This creates a really big crest or a really deep trough.

25. Interference
Destructive interference is where a crest meets a trough. The result is that they cancel each other out leaving no wave.

26. Superposition
The ability of waves to superimpose (add their displacements and energy) as they move through each other.
They carry on after as if the other wave was not present
Eg, if several people in a room talk all at once, the different sounds move from place to place with no effect on each other

27. Superposition

28. Superposition

29. Standing Waves
These are produced when a wave is reflected back on itself
The original wave and it’s reflection interfere to form a standing wave.
They have constant positions of no motion (called a node) and maximum motion (called an antinode) N A

30. 2 Source Interference
Having 2 sources of concentric waves will produce a pattern like this
There appear to be lines radiating out from between the sources

31. 2 Source Interference
Anti-nodal lines are lines of constructive interference. ie the water is choppy
Nodal lines are lines of destructive interference. ie the water is flat

32. 2 Source Interference The n value is called the path difference
It tells you how many wavelengths further one wave has traveled compared to the other

33. 2 Source Interference
If the waves were sound, a person walking from A to B would hear a series of loud and soft noises as they moved across the antinodal and nodal lines A B

34. Light Visible Light is part of the electromagnetic spectrum.
Gamma Rays
High Energy
High Frequency
Short Wavelength
X-rays
Ultra Violet (UV)
Visible Light
Infra-red
Radio Waves
Microwaves
Low Energy
Low Frequency
Long Wavelength

35. Colour

36. Light In general, light travels in straight lines
Light spreads out in all directions from it’s source.
The further from the source the less the illumination
Light Source

37. Reflection
A light ray can be bounced off a flat surface. This is called reflection.
Law of Reflection: The angle of incidence = the angle of reflection. (Remember: angles are measured from the normal) qi qr

38. Plane Mirrors To form images, light rays have to meet or focus.
The image is laterally inverted by a plane mirror (ie. You wave left hand, image waves right)
The image is virtual. It is formed behind the mirror, in a place where no light actually went. (a real image is formed when light rays meet at a point)

39. Plane Mirrors Eye sees image back here
Light from object reflects into eye
Eye sees image back here
Plane Mirrors
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40. Curved mirrors The centre of the mirror is called the pole.
A line at right angles to this is called the principal axis.
The focal length of a mirror is half the radius of curvature
The radius of curvature is the radius of the ball that the mirror would have been cut from

41. Curved Mirrors C = centre of curvature c = radius of curvature
F = Focal point or focus f = focal length
pa = principal axis P = pole C F P c pa f

42. Concave Mirrors
Concave (or converging) mirrors focus light at the focal point.

43. Convex Mirrors Convex mirrors have a focal point behind the mirror.
Convex (or diverging) mirrors spread the light rays apart so that they appear to have come from the focal point

44. Ray Diagrams Used to find the size, nature and position of images.
The nature of an image formed by a mirror or lens can be described according to 3 characteristics: Is it
a) upright or inverted
b) magnified, diminished or the same size
c) Real or virtual

45. Ray Diagrams
Rule One: An incident ray parallel to the pa is reflected back through the focal point.

46. Ray Diagrams
Rule Two: An incident ray headed towards the pole reflects back at an equal angle

47. Ray Diagrams
Rule Three: An incident ray that passes through the focal point on the way to the mirror is reflected back parallel to the pa.

48. Ray Diagrams All three combined allow you to find the image.
In this example the image is inverted, diminished and real.

49. Ray Diagrams
The same can be applied to convex mirrors with a few small changes…
All convex mirror images are virtual.

50. Mirror Formulae Descartes’ Formula: Or: m=magnification factor
h=height of image or object
d=distance from mirror to image or object
Distances behind the mirror are negative

51. Mirror Formulae Newton’s Formula: Or:
S=distance from focal point to image or object
All distances are positive but care must be taken calculating Si or So. It is usually necessary to sketch a ray diagram to check.
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52. Refraction of Light
The bending of light as it goes from one medium into another.
Angle of Incidence
Angle of Refraction

53. Snell’s Law Where: n= refractive index
q= angle of incidence/refraction
v= wave speed
l= wavelength
Medium 1 is the one the light is leaving.
Medium 2 is the one it is entering.
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54. Total Internal Reflection
When light travels from a high to low refractive index, it bends away from the normal.
A particular angle of incidence will cause the light to refract at 90º, ie along the boundary between the media.

55. Total Internal Reflection
This angle of incidence is called the critical angle qc.
This can be calculated by putting qr= 90º into Snell’s Law. qc
Angle of Refraction=90º

56. Total Internal Reflection
If the critical angle is exceeded, the light will reflect off the inside surface of the medium it is trying to escape from.
This is called Total Internal Reflection.
qi> qc
Reflected ray

57. Total Internal Reflection
This is the principle behind fibre optic cables which are used in medicine and communications.
Fibre optic cable
Light ray
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58. Dispersion
Because white light is made up of a spectrum of colours of slightly different wavelengths, they all refract at a slightly different angle.
This causes dispersion of the white light into it’s spectrum colours.
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59. Lenses There are two main types:
Convex (or converging) lens – this brings the rays together.
They have a principal focus behind the lens. F

60. Lenses Concave (or diverging) lens – these spread the rays apart.
They have a principle focus in front of the lens F

61. Lenses
Descartes’ and Newton’s formulae still apply as do the ray diagram rules, to find the size, nature and position of the image formed by a lens.
Eg: F

62. Lenses
Note: When using Newton’s formula for a convex lens, So is the distance from object to near focus, and Si from image to far focus
When using Newton’s formula for a concave lens, So is the distance from object to far focus, and Si from image to near focus
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