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Electromagnetic Waves Physics 202 Professor Vogel (Professor Carkner’s notes, ed) Lecture 12

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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 The new electric field becomes: E = E 0 cos Since I depends on E 2 it becomes: I = I 0 cos 2 This is only true for polarized light 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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Polarization By Reflection Light reflected off of a surface is generally polarized This is why polarized sunglasses reduce glare 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 and Refraction When light passes from one medium to another (e.g. from air to water) it will generally experience both reflection and refraction Reflection is the portion of the light that does not penetrate the second medium but bounces off of the surface 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 ): the angle between the incident ray and the normal Angle of reflection ( 1 ’): the angle of the reflected ray and the normal Angle of refraction ( 2 ): the angle of the refracted ray and the normal

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Laws Law of Reflection The angle of reflection is equal to the angle of incidence ( 1 ’ = 1 ) Law of Refraction The angle of refraction is related to the angle of incidence by: 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 = 1 for vacuum We will approximate air as n = 1 also n is always greater than or equal to 1 Large n means more bending

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

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Total Internal Reflection Consider the case where 2 = 90 degrees In this case the refracted light is bent parallel to the interface For angles greater than 90 there is no refraction and the light is completely reflected 2 > 90 when the incident angle is greater than the critical angle c 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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Chromatic Dispersion The index of refraction depends on the wavelength of light In general, n is larger for shorter wavelengths Blue light bent more than red Incident white light is spread out into its constituent colors Chromatic dispersion with raindrops causes rainbows

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Chromatic Dispersion

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Brewster Angle At a certain angle, known as the Brewster angle, the reflected light is totally polarized At B the reflected and refracted rays are perpendicular to each other, so B + r = 90 Since n 1 sin B = n 2 sin r we get B = tan -1 (n 2 /n 1 ) If we start out in air n 1 = 1 so: B = tan -1 n This is Brewster’s Law

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