Lecture 8 Polarization

Instructor: Kazumi Tolich Lecture 8

¨ Reading chapter 31-4 to 31-7 ¤ Polarization n By absorption n By reflection n By scattering n By birefringence (double refraction) Quiz: 1

3 Demo 1

¨ Linear Polarization Vector Model Quiz: 2

5 Malus’ law

¨ Consider that an polarized wave is passed

through a polarizing filter (polarizer), and the The incident light is polarized at Transmission angle θ with respect to the transmitted wave is then passed through a axis transmission axis. second polarizing filter (analyzer).

¨ The intensity of the transmitted wave depends on the angle θ between the transmission axis and the incident plane of polarization.

¨ The relation for intensity is called Malus’ Law: � = � cos � Demo 2

¨ Polaroid Sheets ¤ Demonstration of transmission intensity and angle between the polarizer and analyzer. Quiz: 3 Example 1

¨ Two polarizing sheets have their transmission axes crossed so that no light is transmitted. A third sheet is inserted so that its transmission axis makes an angle θ with the transmission axis of the first sheet. The light incident on the first sheet is unpolarized. a) Derive an expression for the intensity of the transmitted light as a function of θ. b) Show that the intensity transmitted through all three sheets is maximum when θ = 45º. Index of refraction

¨ The speed of light in a transparent medium is less than the speed of light in vacuum. ¨ A transparent medium is characterized by an index of refraction, n, given by

¤ c: speed of light in vacuum ¤ v: speed of light in the medium Polarization by reflection

¨ When unpolarized light is reflected from a surface boundary between two transparent media, the reflected light is partially polarized.

¨ If the incidence angle is polarizing angle, θp, the reflected light is completely polarized. n1 � tan � = n � 2 ¨ At the polarizing angle, the reflected and refracted rays are perpendicular to each other.

¨ Note that the transmitted ray is only partially polarized. Polarized incident ray

¨ If the incident light itself is polarized with the electric field in the plane of incidence, no reflected light exists when the angle of

incidence is θp. Demo 3

¨ Polarization by Reflection (Polaroid Sheet) ¤ Demonstration of how sunglasses with a polarizing sheet can cut out the reflection of sunlight off a lake, sea, or snow surface. Scattering of light

¨ Small particles and molecules absorb light and reradiate in all directions.

¨ This phenomenon is called scattering. Why is the sky blue?

¨ The molecules in the atmosphere scatter sunlight (Rayleigh scattering).

¨ The intensity of the scattered light depends on 1/λ4, making the intensity much higher for color with shorter λ (i.e. violet and blue). ¨ The sunlight does not contain a lot of violet, and human eyes are not as sensitive to violet light as to blue light. ¨ The sunset is red because the colors of shorter wavelength have scattered away before reaching your eyes because the light travels a longer distance in the atmosphere. Polarization by scattering

¨ The charges in a scattering atom act as electric dipole antennas.

¨ The electric field vector of the scattered light perpendicular to the initial direction of propagation is perpendicular to directions of propagation of light before and after scattering.

¨ Bees use this sky polarization to navigate. Demo 4

¨ Polarization by Scattering Light in birefringent material

¨ When light rays are propagating in a special direction called the optic axis in a birefringent material, all the rays propagate with the same speed.

¨ When light is incident at an angle to the optic axis, the rays are separated into two rays, the ordinary ray and the extraordinary ray, which are polarized in mutually perpendicular directions, and travel in different directions and emerge separated in space. Demo 5

¨ Polarization by Birefringence ¤ Demonstration of polarization by birefringence. ¤ The two emerging rays are mutually perpendicularly polarized. ¤ If the material is rotated, the extraordinary ray revolves in space around the ordinary ray. Polarization by birefringence

¨ If light is incident perpendicularly on the crystal face and the optic axis, the two rays travel in the same direction but at different speeds (and wavelengths). ¨ The rays emerge with a phase difference that depends on the thickness of the plate. ¤ In a quarter-wave plate, the rays emerge with a phase difference of 90º. ¤ In a half-wave plate, the rays emerge with a phase difference of 180º. Circular polarization by birefringent material

¨ Suppose that the incident light is linearly polarized so that the E field vector is at 45º to the optic axis of a quarter-wave plate (causes 90° phase difference).

¨ The E field vector of the emerging ray rotates in a circle, or is circularly polarized.

¨ � = � sin �� ¨ � = � sin �� + 90° = � cos �� Demo 6

¨ Circular Polarization Vector Model ¤ In a circularly polarized ray, the electric field “corkscrews” through space with either a right- handed or left-handed twist. ¤ On reflection, circular polarization reverses direction. Rotating polarization direction by birefringent material

¨ Suppose that the incident light is linearly polarized so that the E field vector is at 45º to the optic axis of a half-wave plate (causes 180º phase difference).

¨ The E field vector of the emerging ray is rotated by 90º relative to that of the incident light.

¨ � = � sin ��

¨ � = � sin �� + 180° = −� sin �� Demo 7

¨ Polarization by Stress in Plastic ¤ Stressed plastic becomes birefringent. ¤ Angle of polarization depends on the color (wavelength) of light.