# Electromagnetic Waves Physics 202 Professor Lee Carkner Lecture 21.

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Electromagnetic Waves Physics 202 Professor Lee Carkner Lecture 21

PAL #20 EM Radiation  Acceleration of lightsail craft  F = ma = p r A a = p r A/m   I = P s /4  r 2 = (3.9X10 26 )/(  (1.5X10 11 ) 2 ) = 1379 W  p r = (2)(1379)/(3X10 8 ) = 9.2X10 -6 N/m 2   Time to get to moon  d = ½at 2   t = 43054 sec ~ 12 hours  Problems   How do you stop or go back?  Gravity and inherited motion also important

Polarization   The plane containing the E vectors is called the plane of oscillation   Most light sources are unpolarized  Any given wave has a random plane of oscillation

Plane of Oscillation x y z y z E E

Direction of Polarization

Unpolarized Light

Polaroid   Polaroid is a sheet of material that will only pass through the components of the E vectors in a certain direction   If you put a horizontal Polaroid sheet on top of a vertical Polaroid sheet no light gets through

Polarizing Sheet

Polarization and Intensity   The sum of all of the y components should be equal to the sum of all of the z components  I = ½ I 0   What about polarized light hitting Polaroid?

Angle of Polarization

Incident Polarized Light  For polarized light incident on a sheet of Polaroid, the resultant intensity depends on the angle  between the original direction of polarization and the sheet  E = E 0 cos   I = I 0 cos 2    For unpolarized light that pass through two polarizing sheets,  is the angle between the two sheets

Multiple Sheets

Sheet Angles

Means of Polarization  A sheet of Polaroid has long molecules embedded in it all aligned in one direction   A similar effect is seen in light passing through interstellar dust clouds    Light can also be polarized by reflection

Reflection and Refraction

 When light passes from one medium to another (e.g. from air to water) it will generally experience both reflection and refraction   Refraction is the bending of the portion of the light that does penetrate the surface

Geometry  The normal line is a line perpendicular to the interface between the two mediums  Angles  Angle of incidence (  1 ):   Angle of reflection (  1 ’):  Angle of refraction (  2 ):

Reflection and Refraction

Laws  Law of Reflection   Law of Refraction  n 2 sin  2 = n 1 sin  1  Where n 1 and n 2 are the indices of refraction of the mediums involved

Index of Refraction  Every material has an index of refraction that determines its optical properties    n is always greater than or equal to 1 

General Cases  n 2 = n 1  No bending   e.g.  n 2 > n 1  Light is bent towards the normal   e.g.  n 2 < n 1  Light is bent away from the normal   e.g. 

Refraction Angles

Total Internal Reflection  Consider the case where  2 = 90 degrees   For angles greater than 90 there is no refraction and the light is completely reflected  n 1 sin  c = n 2 sin 90  c = sin -1 (n 2 /n 1 )  This is the case of total internal reflection, where no light escapes the first medium

Internal and External Reflection

Prism

Chromatic Dispersion  The index of refraction depends on the wavelength of light   Blue light bent more than red   Chromatic dispersion with raindrops causes rainbows

Refraction and Wavelength

Chromatic Dispersion

Polarization By Reflection    When unpolarized light hits a horizontal surface the reflected light is partially polarized in the horizontal direction and the refracted light is partially polarized in the vertical direction

Reflection Polarization

Brewster Angle  At a certain angle, known as the Brewster angle, the reflected light is totally polarized   B +  r = 90   B = tan -1 (n 2 /n 1 )  :  B = tan -1 n  This is Brewster’s Law