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

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

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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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.

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

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

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)

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.

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

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

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.

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

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

Superposition

Superposition

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

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

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

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

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

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

Colour

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

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

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)

Plane Mirrors Eye sees image back here Light from object reflects into eye Eye sees image back here Plane Mirrors Do Page 187 Questions 12A

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

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

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

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

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

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

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

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.

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

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

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

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. Do Page 195 Questions 12B

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

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. Do Page 203 Questions 13A

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.

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

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

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

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

Lenses There are two main types: Convex (or converging) lens – this brings the rays together. They have a principal focus behind the lens. F

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

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

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