Electromagnetic Waves

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

2. 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 • The new electric field becomes: E = E0 cos q • Since I depends on E2 it becomes: I = I0 cos2q • This is only true for polarized light • For unpolarized light that pass through two polarizing sheets, q is the angle between the two sheets

3. Multiple Sheets

4. Sheet Angles

5. 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

6. Reflection andRefraction • 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

7. Geometry • The normal line is a line perpendicular to the interface between the two mediums • Angles • Angle of incidence (q1): the angle between the incident ray and the normal • Angle of reflection (q1’): the angle of the reflected ray and the normal • Angle of refraction (q2): the angle of the refracted ray and the normal

8. Laws • Law of Reflection • The angle of reflection is equal to the angle of incidence (q1’ = q1) • Law of Refraction • The angle of refraction is related to the angle of incidence by: n2 sin q2 = n1 sin q1 • Where n1 and n2 are the indices of refraction of the mediums involved

9. 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

10. General Cases • n2 = n1 • No bending • q2 = q1 • e.g. air to air • n2 > n1 • Light is bent towards the normal • q2 < q1 • e.g. air to glass • n2 < n1 • Light is bent away from the normal • q2 > q1 • e.g. glass to air

11. Total Internal Reflection • Consider the case where q2 = 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 • q2 > 90 when the incident angle is greater than the critical angle qc 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

12. 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

13. Chromatic Dispersion

14. Brewster Angle • At a certain angle, known as the Brewster angle, the reflected light is totally polarized • At qB the reflected and refracted rays are perpendicular to each other, so qB + qr = 90 • Since n1 sin qB = n2 sin qr we get qB = tan-1 (n2/n1) • If we start out in air n1 = 1 so: qB = tan-1 n • This is Brewster’s Law