7Radiation pressureThe theory of relativity: anything moving at the speed of light will carry momentum p=E/cLight can push stuff!My total energy output per unit time is constantMy energy output per unit time and area drops as the distance2RNear Earth:P~ N/m2
8PolarizationWhen E points in one direction the wave is linearly polarizedPoints out of the screen●EEThere are materials that absorb waves when E points in one directionThere are also other polarizations for which E changes direction… but not in the other
9I=I1 cos2 q Polarizers at angles reduce the intensity I=I0 I=I1=I0/2 Selects one polarizationOnly the projection onto the transmission axis gets throughI=I1 cos2 q
10Crossed polarizers transmit approximately what fraction of an electromagnetic wave? 0%25%50%75%100%
11YOUNG’S INTERFERENCE EXPT. What is light?I believe light is a stream of fast moving particles. This explains why and how light reflects and refracts.NewtonI can also understand how and why light reflects and refracts if I assume it is a wave.HUYGENS’ PRINCIPLEHuygensIf light is a wave it can should be able to go around small obstacles…and it does!YOUNG’S INTERFERENCE EXPT.My equations predicted that light is a high frequency electromagnetic wave in1865.T. YoungMaxwell
12So, is light a wave or a particle? EinsteinIn many cases light behaves like a wave, but sometimes (when quantum effects are important) it behaves like a particle.So, is light a wave or a particle?Since it sometimes behaves like one and sometimes like the other it is neither.Instead of trying to force it into some label convenient to us we should find out its properties.Fermat
13The ray approximationLight behaves as a ray. In uniform media it travels in a straight lineWhen light propagates its wave nature is hidden ifWe never look at distances of the order of l (or smaller)All obstacles have typical sizes much larger than lThe wave nature of light is not important for d >> l
14For smaller distances (d ~ l) the wave nature begins to show up The ray approximationFor smaller distances (d ~ l) the wave nature begins to show upFor d << l the wave nature is central in understanding light’s behaviorWhen looking at features smaller than l the interference of light waves shows up
15This is the shortest path The shortest time principle – FERMAT’S PRINCIPLEWhen light behaves as a ray and travels from point A to point B itfollows the path that gets it to B in the shortest time possibleIn a uniform medium where the light speed is c1 …… for constant speed the shortest path takes the least amount of timeIn uniform media light rays travel in straight linesThis is the shortest pathAThis path is longerB
16Speed of light in the medium When light behaves as a ray and travels from point A to point B itfollows the path that gets it to B in the shortest time possibleLet us look at a reflected rayLABx is such that it takes the least amount of time to go from A to BhSpeed of light in the mediumxmirrorL - x
17II. The path of a light ray is reversible. I. The law of reflectionq1 = q1II. The path of a light ray is reversible.III. The path of a light ray in vacuum defines what is meant by “a straight line”.
1825.17The reflecting surfaces of two intersecting flat mirrors are at an angle of θ. If a light ray strikes the horizontal mirror, show that the emerging ray will intersect the incident ray at an angle of β=180º-2
19Exercise 25.17This looks like an application to the reflection formula and a bit of geometrya-qb =(p-q-a)+(a-q)=p-2qp-q-abqaa
20When light behaves as a ray and travels from point A to point B it follows the path that gets it to B in the shortest time possibleLook at a ray going form one medium with v1 to another with v2v1v2ABhxL - x
21Index of Refraction v1 v2 Define the index of refraction: A BThen under refraction,
22Snell’s law of refraction n2 sinq2 = n1 sin q1n1n2
23longer than equal to shorter than perpendicular to parallel to Given two slabs of transparent material of equal thickness, Fermat’s principle means that the part of a ray passing through the medium with the higher index of refraction is ______ the part passing through the lower index medium.longer thanequal toshorter thanperpendicular toparallel to
2425.13When the light in the figure passes through the glass block, it is shifted laterally by the distance d. If n = 1.76, find the value of d.
25Exercise 25.13This looks like an application to the refraction formula and a bit of geometryq1q1 -q2hLq2d
26Total internal reflection When light goes from medium 1 to medium 2 with n1 > n2Larger than 1If we increase q1 the right hand side growsEventually, when sinq1 = n2/n1 we get sinq2=1If we increase q1 beyond that the wave in medium 2 disappearsThe ray sufferstotal internal reflectionθc is when sinθ2=1 i.e. n1/n2 sin θc =1
27Find the critical angle for a ray of light in glass Air: n2 = 1 Glass: n1 = > qc = 42oFiber Opticsclad, n2 < n1Two Rt Angle PrismsNo Loss of Light; use inoptical instrumentscore, n1
28Constructive interference creates the new wave front. Huygen’s principle (1678)Each point on a wave front is a source of secondary spherical wavelets.Constructive interference creates the new wave front.
29Endoscope "Foreign Body" in the Stomach Swallowed Quarter Here is a quarter which a youngman swallowed and which is lyingin the stomach. These are easilyremoved with a wire snare ordevice for grasping a coin.
3824.26A possible means of space flight is to place an absorbing sheet into orbit around the Earth and then use the light from the Sun to push this “solar sail.” Suppose a sail of area 6105 m2 and mass 6000kg is placed in orbit facing the Sun.a) what is the force exerted on the sail?b) What is the sail’s acceleration?c) How long does it take the sail to reach the Moon, 3.84108 m away? Ignore all gravitational effects, assume that the acceleration calculated in part b) remains constant, and assume a solar intensity of 1340 W/m2
4024.35An important news announcement is transmitted by radio waves to people sitting next to their radios, 100 km from the station, and by sound waves to people sitting across the news room, 3M from the newscaster. Who receives the news first? Explain. Take the speed of sound in air to be 343 m/s.
41Exercise 24.35the sound and radio waves start at the same timesound covers a distance d in a time d/vradio waves cover a distance L in a time L/cLight wins
4224.41In the figure, suppose that the transmission axes of the left and right polarizing disks are perpendicular to each other.Also, let the center disk be rotated on a the common axis with angular speed . Show that if unpolarized light is incident on the left disk with an intensity Imax, the intensity of the beam emerging from the right disk isThis means that the intensity of the emerging beam is modulated at a rate four times the rate of rotation of the center disk. Hint: Use the trig. identitiescos2=(1+ cos2)/2 and sin2=(1- cos2)/2
43Exercise 24.41 q p/2-q p/2-q Imax c is so large that the polarizers appear frozen to a “bit” of light... At time t the rotation angle will be q=wtthe intensity is decreased by (cos q)2qp/2-qp/2-qImaxPolarization after the 3rd polarizerPolarization after the 2nd polarizerPolarization after the 1st polarizer