Wave Optics A knowledge of the properties of light allows us to understand the blue color of the sky and the design of optical devices… PolarizationInterferenceDiffraction

Wave Optics Why is the sky blue? Why is sunset red?

Dual Nature In Newton’s time: light consisted of streams of particles. In 1873, Maxwell predicted the light is a sort of electromagnetic waves. In 1887, Hertz showed light is an electromagnetic wave. Thomas young also prove the wave properties of light.

Particle Model : The straight line traveling of light, reflection and refraction, emission and absorption of light. Wave Model : polarization, interference and diffraction of light.

polaroid reflection birefringence Producing of polarized light phenomena Polarization of light application Chap 34 Polarization of light

Chap 34 The nature and propagation of light Key Terms: Optics Physical optics Wave front Ray Reflection Refraction Specular/diffuse reflection Index of refraction Critical angle Total internal reflection Linear polarization Polarizing filter Dichroism Polarizing axis Malus’s law Brewster’s law Birefringence

transverse waveLongitudinal wave 1. polarization 1.1 What is polarization? Polarization is characteristic of all transverse waves

1.2 polarization status of light Unpolarized light: natural light Polarized light: Linearly polarized light partial polarized light circular polarized light elliptic polarized light

When a wave has only y-displacements (or z), we say it is linearly polarized in this direction. Linearly polarized light

The waves emitted by any one molecule may be linearly polarized, but any actual light source contains a tremendous number of molecules with random orientations, so the emitted light is a random mixture of waves linearly polarized in all possible transverse directions. natural light (unpolarized light)

partially polarized light Linearly polarized light “+” natural light circular and elliptical polarized light

2. How to get polarized light Polarization by polaroid polarization by reflection polarization by birefringence

 2.1 Polarization by polaroid. Nature light Polarizing axis Linearly polarized light

 Malus’s law If the intensity of incident polarized light is I 0, and the polarizing axis makes an angle  with the displacement of the incident light, the intensity of the light transmitted through the polarizer is: I=I 0 cos 2  I=(E o cos  ) 2 = I o cos 2   EoEo I o = E o 2 E o cos 

Polarizing filter can absorb one of the polarized components, and transmit the components that is polarized parallel to a certain axis,called the polarizing axis. And the transmitted intensity : I=I o cos 2 .(for natural light: I=I o /2 )

Example: The natural light has intensity I 0. Find the intensity transmitted by the second polarizer if the angle between the axes of the two filters is Solution:

Example: The incident light is a mixture of natural light with intensity I 1 and linear polarized light with intensity I 2, find the transmitted intensity by the second polarizer. Solution:

2.2 polarization by reflection For most angles of incidence: Reflected light: partially polarized (  >//) Refracted light: partially polarized (//>  ) At one angle of incidence, called the polarizing angle: Reflected light: completely polarized (  ) Refracted light: partially polarized (//>  )  : reflected and refracted //: only refracted

 Brewster’s law Brewster discovered that when  p equals the polarizing angle, the reflected ray and the refracted ray are perpendicular to each other. From the polarizing angle: sin  b = cos  p From the law of refraction: sin  p / sin  b =n b / n a Then: tan  p =n b / n a The natural light is refracted again and again by a stack of glasses, with incidence angle equals the polarizing angle.

Discussion: 2) tell the difference of critical angle and brester angle total internal reflection.  1) Reflected light: completely polarized (  )  Refracted light: partially polarized (//>  )  reflected ray is perpendicular to refracted ray brester angle critical angle

Polarization by reflection is the reason polarizing filters are widely used in sunglasses, cameras…

draw the reflected light and refracted light n1n1 n2n2 i i n1n1 n2n2 n1n1 n2n2 n1n1 n2n2 i i0i0 i0i0 i0i0 n1n1 n2n2 n1n1 n2n2

2.3 polarization by birefringence Birefringence: the material has different indexed of refraction for different directions of polarization. Here are some examples: Extraordinary light Ordinary light Calcite crystal ( 方解石晶体 ):

 3. scatter  Why the sky looks blue,and sunsets are red?