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Electromagnetic Waves Physics 202 Professor Lee Carkner Lecture 21

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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

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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

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Plane of Oscillation x y z y z E E

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Direction of Polarization

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Unpolarized Light

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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

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Polarizing Sheet

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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?

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Angle of Polarization

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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

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Multiple Sheets

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Sheet Angles

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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

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Reflection and Refraction

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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

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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 ):

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Reflection and Refraction

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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

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

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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.

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Refraction Angles

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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

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Internal and External Reflection

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Prism

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

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Refraction and Wavelength

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Chromatic Dispersion

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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

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Reflection Polarization

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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

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