Chapter 33 cont. The Nature of Light and Propagation of Light (lecture 2) Dr. Armen Kocharian

Transcription

1 Chapter 33 cont The Nature of Light and Propagation of Light (lecture 2) Dr. Armen Kocharian

2 Polarization of Light Waves The direction of polarization of each individual wave is defined to be the direction in which the electric field is vibrating In this example, the direction of polarization is along the y-axis

3 Unpolarized Light, Example All directions of vibration from a wave source are possible The resultant em wave is a superposition of waves vibrating in many different directions This is an unpolarized wave The arrows show a few possible directions of the waves in the beam

4 Polarization of Light, cont. A wave is said to be linearly polarized if the resultant electric field E vibrates in the same direction at all times at a particular point The plane formed by E and the direction of propagation is called the plane of polarization of the wave

5 Methods of Polarization It is possible to obtain a linearly polarized beam from an unpolarized beam by removing all waves from the beam except those whose electric field vectors oscillate in a single plane Processes for accomplishing this include selective absorption reflection double refraction scattering

6 Polarization by Selective Absorption The most common technique for polarizing light Uses a material that transmits waves whose electric field vectors lie in the plane parallel to a certain direction and absorbs waves whose electric field vectors are perpendicular to that direction

7 Active Figure (SLIDESHOW MODE ONLY)

8 Selective Absorption, cont. E. H. Land discovered a material that polarizes light through selective absorption He called the material polaroid The molecules readily absorb light whose electric field vector is parallel to their lengths and allow light through whose electric field vector is perpendicular to their lengths

9 Selective Absorption, final It is common to refer to the direction perpendicular to the molecular chains as the transmission axis In an ideal polarizer, All light with E parallel to the transmission axis is transmitted All light with E perpendicular to the transmission axis is absorbed

10 Intensity of a Polarized Beam The intensity of the polarized beam transmitted through the second polarizing sheet (the analyzer) varies as I = I max cos 2 θ (Malus s Law) I o is the intensity of the polarized wave incident on the analyzer Malus s law applies to any two polarizing materials whose transmission axes are at an angle of θ to each other

11 Intensity of a Polarized Beam, cont. The intensity of the transmitted beam is a maximum when the transmission axes are parallel θ = 0 or 180 o The intensity is zero when the transmission axes are perpendicular to each other This would cause complete absorption

12 Intensity of Polarized Light, Examples On the left, the transmission axes are aligned and maximum intensity occurs In the middle, the axes are at 45 o to each other and less intensity occurs On the right, the transmission axes are perpendicular and the light intensity is a minimum

13 Polarization by Reflection When an unpolarized light beam is reflected from a surface, the reflected light may be Completely polarized Partially polarized Unpolarized It depends on the angle of incidence If the angle is 0, the reflected beam is unpolarized For other angles, there is some degree of polarization For one particular angle, the beam is completely polarized

14 Polarization by Reflection, cont. The angle of incidence for which the reflected beam is completely polarized is called the polarizing angle, θ p Brewster s law relates the polarizing angle to the index of refraction for the material sin θp n = = tan θp cos θ p θ p may also be called Brewster s angle

15 Polarization by Reflection, Partially Polarized Example Unpolarized light is incident on a reflecting surface The reflected beam is partially polarized The refracted beam is partially polarized

16 Polarization by Reflection, Completely Polarized Example Unpolarized light is incident on a reflecting surface The reflected beam is completely polarized The refracted beam is perpendicular to the reflected beam The angle of incidence is Brewster s angle

17 Polarization by Double Refraction In certain crystalline structures, the speed of light is not the same in all directions Such materials are characterized by two indices of refraction They are often called double-refracting or birefringent materials

18 Polarization by Double Refraction, cont. Unpolarized light splits into two planepolarized rays The two rays are in mutual perpendicular directions Indicated by the dots and arrows

19 Polarization by Double Refraction, Rays The ordinary (O) ray is characterized by an index of refraction of n o This is the same in all directions The second ray is the extraordinary (E) ray which travels at different speeds in different directions Characterized by an index of refraction of n E that varies with the direction of propagation

20 Polarization by Double Refraction, Optic Axis There is one direction, called the optic axis, along which the ordinary and extraordinary rays have the same speed n O = n E The difference in speeds for the two rays is a maximum in the direction perpendicular to the optic axis

21 Some Indices of Refraction

22 Optical Stress Analysis Some materials become birefringent when stressed When a material is stressed, a series of light and dark bands is observed The light bands correspond to areas of greatest stress Optical stress analysis uses plastic models to test for regions of potential weaknesses

23 Polarization by Scattering When light is incident on any material, the electrons in the material can absorb and reradiate part of the light This process is called scattering An example of scattering is the sunlight reaching an observer on the Earth being partially polarized

24 Polarization by Scattering, cont. The horizontal part of the electric field vector in the incident wave causes the charges to vibrate horizontally The vertical part of the vector simultaneously causes them to vibrate vertically If the observer looks straight up, he sees light that is completely polarized in the horizontal direction

25 Scattering, cont. Short wavelengths (blue) are scattered more efficiently than long wavelengths (red) When sunlight is scattered by gas molecules in the air, the blue is scattered more intensely than the red When you look up, you see blue At sunrise or sunset, much of the blue is scattered away, leaving the light at the red end of the spectrum

26 Optical Activity Certain materials display the property of optical activity A material is said to be optically active if it rotates the plane of polarization of any light transmitted through it Molecular asymmetry determines whether a material is optically active

27 Huygens s Principle Huygens assumed that light is a form of wave motion rather than a stream of particles Huygens s Principle is a geometric construction for determining the position of a new wave at some point based on the knowledge of the wave front that preceded it

28 Huygens s Principle, cont. All points on a given wave front are taken as point sources for the production of spherical secondary waves, called wavelets, which propagate outward through a medium with speeds characteristic of waves in that medium After some time has passed, the new position of the wave front is the surface tangent to the wavelets

29 Huygens s Construction for a Plane Wave At t = 0, the wave front is indicated by the plane AA The points are representative sources for the wavelets After the wavelets have moved a distance cδt, a new plane BB can be drawn tangent to the wavefronts

30 Huygens s Construction for a Spherical Wave The inner arc represents part of the spherical wave The points are representative points where wavelets are propagated The new wavefront is tangent at each point to the wavelet

31 Huygens s Principle and the Law of Reflection The law of reflection can be derived from Huygens s principle AB is a wave front of incident light The wave at A sends out a wavelet centered on A toward D The wave at B sends out a wavelet centered on B toward C AD = BC = cδt

32 Huygens s Principle and the Law of Reflection, cont. Triangle ABC is congruent to triangle ADC cos γ = BC / AC cos γ = AD / AC Therefore, cos γ = cos γ and γ = γ This gives θ 1 = θ 1 This is the law of reflection

33 Huygens s Principle and the Law of Refraction Ray 1 strikes the surface and at a time interval Δt later, ray 2 strikes the surface During this time interval, the wave at A sends out a wavelet, centered at A, toward D

34 Huygens s Principle and the Law of Refraction, cont. The wave at B sends out a wavelet, centered at B, toward C The two wavelets travel in different media, therefore their radii are different From triangles ABC and ADC, we find 1 2 sin BC v Δ t 1 and sin AD v Δ θ = = θ t 2 = = AC AC AC AC

35 Huygens s Principle and the Law of Refraction, final The preceding equation can be simplified to sin θ1 v1 = sin θ2 v2 sin θ1 cn1 n2 But = = sin θ2 cn2 n1 and so n sin θ = n sin θ This is Snell s law of refraction