1 light & waves l2 ncea achievement standard 2.3 text book reference: chapters 12,13 &14

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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 MotionDirection 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: SoundDirection Of Wave PropagationParticle

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: Greek letter “lam-da”)

• Measured in metres

Wavelength

7

Wave Terms

• Wave speed - the speed of wave propagation

• Symbol: v

• Measured in ms-1

• Period - the time it takes one wavelength to pass a given point

• Symbol: T

• Measured in seconds

8

Wave Terms

• Frequency - the number of waves that pass a given point per second

• Symbol : f• Measured in Hertz Hz

(or cycles per second s-1)

• Note: Frequency and Period are inverses of each other

• ie. f =1/T or T = 1/f

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

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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.

WavefrontsRay

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.

fv

Pg 224 Questions 14A 1-6 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

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

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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

angle of incidence/refraction

v= wave speed

wavelength

Medium 1 is the one the wave is leaving.

Medium 2 is the one it is entering.

2

1

2

1

1

2

sin

sin

v

v

n

n

r

i

22

Diffraction

• The bending of waves as they travel through gaps…..

• The smaller the gap, the more the diffraction

Pg 229 Questions 14B 1-6 23

Diffraction• ….or around edges.

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.

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Interference

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

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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

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Superposition

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Superposition

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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)

NN

A

N

A

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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

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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

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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

n=0

n=1

n=1

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

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Light• Visible Light is part of the electromagnetic

spectrum.

Gamma RaysHigh Energy

High Frequency

Short Wavelength

X-rays

Ultra Violet (UV)

Visible Light

Infra-red

Radio Waves

Microwaves

Low Energy

Low Frequency

Long Wavelength

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Colour

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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

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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)

i r

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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)

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Plane Mirrors

Do Page 187 Questions 12A

Light from object reflects

into eye

Eye sees image back

here

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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

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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

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Concave Mirrors• Concave (or converging) mirrors focus light

at the focal point.

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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

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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

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Ray Diagrams• Rule One: An incident ray parallel to the

pa is reflected back through the focal point.

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Ray Diagrams

• Rule Two: An incident ray headed towards the pole reflects back at an equal angle

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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.

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

and real.

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Ray Diagrams• The same can be applied to convex mirrors

with a few small changes…

• All convex mirror images are virtual.

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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

oi ddf

111

o

i

o

i

d

d

h

hm

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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.

2fSS oi

f

S

S

f

h

hm i

oo

i

Do Page 195 Questions 12B

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Refraction of Light• The bending of light as it goes from one medium into another.

Angle of Incidence

Angle of Refraction

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Snell’s Law

• Where:n= refractive index

= angle of incidence/refraction

v= wave speed

= wavelength

Medium 1 is the one the light is leaving.

Medium 2 is the one it is entering.

2

1

2

1

1

2

sin

sin

v

v

n

n

r

i

Do Page 203 Questions 13A

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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.

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Total Internal Reflection

• This angle of incidence is called the critical angle c.

• This can be calculated by putting r= 90º into Snell’s Law.

c

Angle of Refraction=90º

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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.

i> c

Reflected ray

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Total Internal Reflection

• This is the principle behind fibre optic cables which are used in medicine and communications.

Fibre optic cable

Light ray

Do Page 206 Questions 13B

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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.

Do Page 208 Questions 13C

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Lenses• There are two main types:

• Convex (or converging) lens – this brings the rays together.

• They have a principal focus behind the lens.

F

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Lenses

• Concave (or diverging) lens – these spread the rays apart.

• They have a principle focus in front of the lens

F

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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

F

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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

Do Page 210 Questions 13D