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  p r = 2I/c  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  a = (9.2X10 -6 )(2.25X10 8 )/5000 = 0.41 m/s 2  Time to get to moon  d = ½at 2  t = (2d/a) ½ = [(2)(3.8X10 8 )/(0.41)] ½  t = sec ~ 12 hours  Problems  Sunlight only pushes in one direction  How do you stop or go back?  Gravity and inherited motion also important

Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the mass doubles (but the size stays the same)? A)Goes in B)Goes out C)Stays put

Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the mass doubles and the surface area doubles? A)Goes in B)Goes out C)Stays put

Consider a dust grain near a star. If the grain is perfectly balanced between light pressure out and gravity in, what happens to the grain if the distance from the star doubles? A)Goes in B)Goes out C)Stays put

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

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

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  This is true only when the incident light is completed unpolarized  What about polarized light hitting Polaroid?

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   This alignment permits only the components in that direction to pass   The dust grains are partially aligned by the galactic magnetic field and so the light is partially polarized  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   Angles  Angle of incidence (  1 ): the angle between the incident ray and the normal  Angle of reflection (  1 ’):  Angle of refraction (  2 ): the angle of the refracted ray and the normal

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  Large n means more bending

General Cases  n 2 = n 1    2 =  1  e.g. air to air  n 2 > n 1    2 <  1  e.g. air to glass  n 2 < n 1    2 >  1  e.g. glass to air

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

Chromatic Dispersion   In general, n is larger for shorter wavelengths   Incident white light is spread out into its constituent colors  Chromatic dispersion with raindrops causes rainbows

Chromatic Dispersion

Polarization By Reflection  Light reflected off of a surface is generally polarized   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

Brewster Angle   At  B the reflected and refracted rays are perpendicular to each other, so  B +  r = 90   B = tan -1 (n 2 /n 1 )  If we start out in air n 1 = 1 so:  B = tan -1 n 

Next Time  Read:  Homework: Ch 33, P: 37, Ch 34, P: 7, 9, 10, 11, 12, 13, 15