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Electromagnetic Waves Physics 202 Professor Lee Carkner Lecture 21 PAL #20 EM Radiation Acceleration of lightsail craft F = ma = prA a = prA/m pr = 2I/c I = Ps/4pr2 = (3.9X1026)/(4p(1.5X1011)2) = 1379 W pr = (2)(1379)/(3X108) = 9.2X10-6 N/m2 a = (9.2X10-6)(2.25X108)/5000 = 0.41 m/s2 Time to get to moon d = ½at2 t = (2d/a)½ = [(2)(3.8X108)/(0.41)] ½ t = 43054 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 I0 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 q between the original direction of polarization and the sheet E = E0 cos q I = I0 cos2 q For unpolarized light that pass through two polarizing sheets, q 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 (q1): the angle between the incident ray and the normal Angle of reflection (q1’): Angle of refraction (q2): the angle of the refracted ray and the normal Laws Law of Reflection Law of Refraction n2 sin q2 = n1 sin q1 Where n1 and n2 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 n2 = n1 q2 = q1 e.g. air to air n2 > n1 q2 < q1 e.g. air to glass n2 < n1 q2 > q1 e.g. glass to air Total Internal Reflection Consider the case where q2 = 90 degrees For angles greater than 90 there is no refraction and the light is completely reflected n1 sin qc = n2 sin 90 qc = sin-1 (n2/n1) 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 qB the reflected and refracted rays are perpendicular to each other, so qB + qr = 90 qB = tan-1 (n2/n1) If we start out in air n1 = 1 so: qB = tan-1 n Next Time Read: 34.1-34.6 Homework: Ch 33, P: 37, Ch 34, P: 7, 9, 10, 11, 12, 13, 15
