4.4 Wave Behaviors Waves interact with media and each other in variety of ways. Changes in speed or obstacles in their path will change their shape and direction. Reflection Refraction Diffraction Interference

Superposition - Interference

Superposition

Reflection

Reflection Law  Wave reflection occurs when a wave meets a boundary, and is at least partially diverted backwards.  The angles of the rays are always measured with respect to the normal which is perpendicular to the surface.  incident =  reflect

Reflection and refraction  We can also look at the wavefronts: Observe…  During reflection what happens to the frequency and the wavelength.=? 4.4 – Wave behavior reflective surface spherical wavefront flat or straight wavefront reflective surface

Reflected Rays come off hard boundary inverted and reversed in shape.

Refraction occurs when a wave meets a boundary, or a different medium, and is at least partially transmitted. The bending occurs because of a  v. Refraction

Refraction of Wavefronts Which side is faster? How can you tell?

Ex 1. Wavefronts strike the boundary between clear and muddy water and slow down. Sketch some new wavefronts entering the muddy water. CLEAR WATER BOUN DARY INCIDENT WAVE normal MUDDY WATER

CLEAR WATERMUDDY WATER BOUN DARY INCIDENT WAVE REFRACTED WAVE normal  incidence angle of incidence  refraction angle of refraction

Equations of Refraction Frequency is fixed Index of refraction n = c/v. sin  1 /sin  2 = constant = v 1 /v 2 n 1 sin  1 = n 2 sin  2 (Snell’s Law) Do This: Show that n 1 /n 2 = 1 / 2.

Snell’s Law Problem Set

Do Now: A ray of light enters air n=1.00 from water n = 1.33 at an incident angle of 59 o. Calculate the angle of refraction. Sketch: The incident ray, Reflected ray, Refracted ray.

Critical Angle,  c. from slow to fast. It is angle  1 that makes  o. For air, n= 1 so: n 1 sin  c = 1 sin 90 o. sin  c = 1/ n 1.  1 beyond total internal reflection.

Ex: The index of refraction of flint glass is What is the critical angle for light entering air from flint glass?

Ex: The index of refraction of diamond is What is the critical angle for light entering diamond from flint glass? Explain.

Huygen’s Principle Brian Lamore start from 1 min AKt0UU4.3%20JJ%20Wave%20Characteri stics.pptxhttps:// AKt0UU4.3%20JJ%20Wave%20Characteri stics.pptx

Dispersion

Diffraction = bending around boundary.

Size of obstacle

Displacement vs Time

Displacement vs. Distance For a longitudinal: look at the air molecules in their undisturbed positions and compare them as a sound wave passes by. Look at the equilibrium points. See if the particles are displaced left (below) or right (above) or not (0)

Hwk Set

Light is a small part of the EM spectrum. All EM waves have the same behavior.

Light

The Visible Spectrum A range of light waves extending in wavelength from about 400 to 700 namometers.

Light & all EM waves are transverse, non-mechanical waves.

Electromagnetic Wave Velocity The speed c is the same for all forms of EM waves in a vacuum of space. It is ~ 3.0 x 10 8 m/s. In air almost the same. No mass can go the speed of light. Nothing can go faster.

Amplitude is related to the wave energy. So is frequency. High Amplitude means bright. Higher f = higher energy change in color.

What is Light/EM waves 2 Models 1) Particles/Photons Packets of energy 2) Electromagnetic Waves energy-carrying waves emitted by vibrating charges. Light displays both types of behavior.

A wave entering a new material may change its velocity depending on the properties of the materials. This will result in a bending of the wave either toward or away from a perpendicular to the interface.

Law of Refraction - Snell’s Law A ray passing from a faster medium to a slower medium bends toward normal.  i greater than  r. What happens to ?

For light traveling from a slow medium to a faster one, the refracted ray bends away from the normal. The light coming off fish bends at water/air interface.

Refraction of sunlight allows us to see sun a few minutes after it has set below horizon.

Amount of “Bending” The amount of bending of light is dependent on the ratio of the 2 speeds. The greater the  v between the two materials, the greater the bend.

“Absolute index of refraction, n,” is the ratio of the v light in a vacuum to its v in a medium. n =cn= index of refraction vv = velocity in medium c = speed of light in vacuum - 3 x 10 8 m/s

Ex: The speed of yellow light in calcite is 1.97 x 10 8 m/s. What is the absolute index of refraction for calcite?

n = c v 3.00 x 10 8 m/s= 1.52 (no units) 1.97 x 10 8 m/s

Snell’s Law – Law of Refraction Relates angle of incidence, angle of refraction and the 2 indices of refraction as well as velocity. n 1 = sin  2 = v 2. n 2 sin  1 v 1. n 1 = indx refrc med 1. n 2 = indx refrc med 2.  1 = angle of incidence  2 = angle of refraction

n 1 sin  1 = n 2 sin  2. c/v 1 sin  1 =c/v 2 sin  2. sin  1 =sin  2. –v 1 v 2. v 2 = sin  2 v 1 sin  1 2. Show that v 2 = sin  2. v 1 sin  1

3. A ray of light enters diamond (n = 2.42) from glycerol (n=1.47) at an incident angle of 40 o. Make a scaled sketch showing the: Incident ray Reflected Ray Refracted Ray

Read Hamper p92-97 Do IB question sheet and problems on pg 95.

At the boundary the wave is partially: reflected AND partially refracted/transmitted.

Critical Angle When light crosses from slow to fast medium, it bends … from normal Critical angle is a  1 occurs when refracted ray is parallel with boundary & most of the ray is reflected internally.

As  i gets larger, ray bends away from normal at greater & greater angle. Beyond critical angle = total internal reflection occurs.

Note: As wave enters new material its frequency does not change. Frequency is the rate of the vibration of causing the wave. Since the velocity changes, then the wavelength must change to satisfy v = f.

Beyond Critical Angle Total Internal Reflection

Applications & Effects of Refraction

Total Internal Reflection – light can be made to internally reflect in a tube or pipe. None escapes.

Light Pipe

Fiber Optics

Light going from cool to warm air can refract and cause mirages because you sight along a line parallel to the ray.

Road Mirage

Light from sky bends up toward you in hot air. You sight down along line.Image appears to be on ground.

Dispersion

Dispersion – polychromatic (white) light is separated into component colors. Special case of refraction. Occurs b/c different /freq’s travel at dif v in materials other than empty space. Different ’s will be refracted/bent more than others.

Short ’s (high f’s) change velocity & are bent more than long ’s.

Each of light travels a different speed in the prism - each is refracted a different amount. This is dispersion.

Which color/ is least refracted? Which color/ is refracted least?

See ’s

Red Light is affected least. It is the longest, and lowest f. Dispersive Medium’s = one’s in which waves of dif f/ ’s, travel at dif speeds. Ex: glass, water are dispersive vacuum is not dispersive. Polychromatic = many colors ex: white light Monochromatic = one color ex: laser light.

Rainbows-dispersion in droplets

. For ray that hits high drops you see red at the top. Other colors pass above you.

Hwk Text book pg 588 #

Mechanical Universe Optics s42.html#

Huygen’s Principle Model’s wave propagation as if each point on wave front is a source of new circular waves (wavelets). The new wavefront is a line sketched tangent to the curved wavelets.

Every point on a wavefront serves as the source of spherical secondary wavelets, such that the wavefront becomes the envelope of these wavelets. The wavelets have the same frequency and speed as the original wavefront.

Huygen’s Principle Predicts Refractive Angle for wavefronts.

Huygen’s Animation ysicszone/lesson/otherpub/wfendt/h uygens.htm

Huygen’s Principle Predicts Refractive Angle