Review: Laws of Reflection and Refraction Law of Reflection A reflected ray lies in the plane of incidence The angle of reflection is equal to the angle of incidence Medium 1 Law of refraction A refracted ray lies in the plane of incidence The angle of refraction is related to the angle of incidence by Snell’s Law Where λ is the wavelength in vacuum Medium 2

Demo 7A-05 Candle Illusion

Total Internal Reflection All light can be reflected, none refracting, when light travels from a medium of higher to lower indices of refraction. medium 2 medium 1 e.g., glass (n=1.5) to air (n=1.0) But θ1 cannot be greater than 90 degrees ! In general, if sin θ1 > (n2 / n1), we have NO refracted ray; we have TOTAL INTERNAL REFLECTION. Critical angle above which this occurs.

©2008 by W.H. Freeman and Company

Examples Fish’s view of the world Prism used as reflectors (e.g., glass with n=1.5) Optical fiber in air (e.g., glass with n=1.5) in water

READING QUIZ 1 One of the following statements is incorrect. A laser emits light which has a very long coherence length. B) An incandescent lamp emits light that has a coherence length of about three meters. The Helium-Neon laser emits light through Spontaneous Emission of photons from an excited state of Helium. D) The photon energy increases with the frequency of the light.

Chromatic Dispersion The index of refraction of a medium is usually a function of the wavelength of the light. It is larger at shorter wavelengths. Consequently, a light beam consisting of rays of different wavelength (e.g., sun light) will be refracted at different angles at the interface of two different media. This spreading of light is called chromatic dispersion. White light: It consists of components of nearly all the colors in the visible spectrum with approximately uniform intensities. The component of a beam of white light with shorter wavelength tends to be bent more. Spectrometer (such as a prism)

Mirage and Rainbow Mirage rainbow water droplet red is outside. intensity max at 42

Double Rainbow Secondary rainbow Two Interactions Primary rainbow One Interaction

DEMO 7A-20 Effect Of Warm Air on Laser light

Warm up quiz 2 Unpolarized light is incident on two polarizers. The axes of the two polarizers are rotated by 30 degrees with respect to each other. If the intensity of the unpolarized light is IO what is the intensity of the light after it passes through both polarizers? √3/2 IO 1/2 IO 3/8 IO D) 3/4 IO

Polarization of Electromagnetic Waves Polarization is a measure of the degree to which the electric field (or the magnetic field) of an electromagnetic wave oscillates preferentially along a particular direction. Linear combination of many linearly polarized rays of random orientations components partially polarized linearly polarized unpolarized Looking at E head-on unequal y- and z-amplitudes equal y- and z-amplitudes

Polarizer: polarization by absorption An electric field component parallel to the transmission axis is passed by a polarizer; a component perpendicular to it is absorbed. transmission axis dichroism (tourmaline, polaroid,…) So if linearly polarized beam with E is incident on a polarizer as shown, Zero if θ=π/2, or if IO =0 If unpolarized beam is incident instead, Polarization can rotate in time if linearly polarized beams of different phases are combined.

Example: two polarizers This set of two linear polarizers produces LP (linearly polarized) light. What is the final intensity? P1 transmits 1/2 of the unpolarized light: I1 = 1/2 I0 P2 projects out the E-field component parallel to x’ axis: = 0 if θ = π/2 (i.e., crossed)

Demo 7B-22 Two Polarizer Effects

Polarization by Reflection Unpolarized light can be broken into two components of equal magnitude: one with its electric vector perpendicular to the plane of incidence and the other with its electric vector parallel to the plane of incidence. The reflected (or refracted) light is partially polarized: due to difference in the reflectivity of the two components (larger for the perpendicular component). Full polarization occurs at Brewster’s angle where

DEMO 7B-23 Polarization by Reflection

Example: Sunglasses cut down glare transmission axis

10:30 QUIZ 3 November 15, 2011 Light is emitted internally in a fluid which has an index of refraction of refraction n =1.75. At the plane interface with the air, what is the critical angle for total internal reflection? Remember the angles are defined with respect to the normal to the plane interface. A) θC = 44.6o B) θC = 34.8o C) θC = 65.2o D) θC = 27.3o

11:30 QUIZ 3 November 15, 2011 Light is emitted internally in a fluid which has an index of refraction of refraction n =2.10. At the plane interface with the air, what is the critical angle for total internal reflection? Remember the angles are defined with respect to the normal to the plane interface. A) θC = 48.2o B) θC = 14.5o C) θC = 35.2o D) θC = 28.4o