Understanding Light as Electromagnetic Waves: Key Concepts and Applications

1. Light Physics 202 Professor Vogel (Professor Carkner’s & CJV notes, ed) Lecture 10

2. Light • Electromagnetic wave • oscillating electric and magnetic fields – • no material medium that is moving! • energy transfer at speed v (c=3X108 m/s in vacuum) • wavelength = distance between repeats • frequency = # repeats per second l f fl=v v=c in vacuum c=3X108 m/s

3. EM Spectrum

4. Radio > 1 meter penetrates solid objects easily Millimeter (microwave) 1 m - 1 mm used for communication Infrared 1 mm - 700 nm we feel as heat Visible 700-400 nm eyes evolved to see Ultraviolet 400 nm - 100 A higher energy, causes sunburn X-ray 100 A - 0.01 A penetrates soft things but not hard Gamma Ray < 0.01 A hard to produce and dangerous The EM Spectrum

5. The EM Wave • Lets consider light as a wave • What kind of wave is it? • What is oscillating? • An EM wave consists of an electric field wave (E) and a magnetic field wave (B) traveling together • The 2 fields are perpendicular to each other and to the direction of travel • An EM wave is transverse (like string waves) • The field waves are sinusoidal and in phase

6. Wave Equations • We can generalize the waves as: E = Em sin (kx -wt) B = Bm sin (kx -wt) • Nothing is actually moving • There is no string • A changing E field induces a B field • A changing B field induces an E field • The two fields continuously create each other • The speed of the wave is related to the fields: c = E/B

7. Traveling EM Wave

8. Key Constants • Two important constants in E and M are the permittivity constant e0 and the permeability constant m0 • Permittivity is the electric force constant: e0 = 8.85 X 10-12 F/m • In farads per meter • Measure of how electric fields propagate through space • Permeability is the magnetic force constant: m0 = 1.26 X 10-6 H/m • In henrys per meter • Measure of how magnetic fields propagate through space • The wave speed depends on these constants: c = 1/(m0 e0)½

9. Poynting Vector • EM waves transport energy • The amount of energy delivered per unit area per unit time is given as flux: flux = W/m2 = J/s/m2 • Flux for an EM wave can be given by the Poynting vector: S = (1/m0) EB • However, E and B are related by E/B = c so we can rewrite S as: S = (1/c m0) E2

10. Intensity • The value of S depends on where the EM wave is in its cycle • We generally are interested in the time averaged value of S, known as the intensity I = (1/c m0) Erms2 • Where Erms is the root-mean-square value of the electric field

11. Radiation Pressure • EM waves exert a pressure on objects • If someone shines a flashlight on you, the light is trying to push you away • like ball bouncing off object pushes object back • The force is very small in most cases • EM pressure is due to the fact that light has momentum which can be transmitted to an object through absorption or reflection

12. Momentum Transfer • The change in momentum due to light is given by: Dp = DU/c • Where Dp is the momentum change and DU is the energy change • The above equation is for absorption • For reflection the momentum change is twice as much: Dp = 2DU/c

13. Light Pressure • From Newton’s second law F = Dp/Dt • The amount of energy delivered in time Dt is: DU = I A Dt • where I is the intensity and A is the area • Since pressure (pr) is force per unit area the pressure becomes: pr = I/c (total absorption) pr = 2I /c (total reflection)

14. Comet Hale-Bopp

15. Comet Tails

16. Light Sail

17. Color Vision • Rods and cones • one type of cone responds to long l’s: “R” • one type of cone responds to mid wavelengths: “G” • one type of cone responds to short l’s: “B” • How our eyes view pure waves: • red : R-type responds • green : G-type responds • blue : B-type responds • yellow : R- and G-types respond • Cyan: G- and B-types respond

18. Color Addition • How our eyes view mixtures : • blue + red: R- and B-types respond • magenta • green + blue : G- and B-types respond • indistinguishable from cyan • red + green : R- and G-types respond • indistinguishable from yellow (Like no pure color) • Demo of color addition -- HELP

19. Color Addition • How our eyes view mixtures : • red + green : R- and G-types respond • indistinguishable from yellow • red + green + blue : R-, G-, and B-types respond • white • yellow + blue : R-, G-, and B-types respond • white

20. Color Subtraction • How our eyes view pigments (absorb light) • white - blue: R- and G-types respond • pigment that absorbs blue looks yellow • white - red : G- and B-types respond • pigment that absorbs red looks cyan • white - (blue + red): G-type responds • pigment that absorbs blue and red looks green

21. Color Subtraction • How our eyes view pigments: • white - (blue + red): • pigment that absorbs blue and red looks green • Pigment: yellow + cyan: • pigments that absorb blue and red look green • A demo of subtraction • usflag-neg.gif

22. primary color red green blue Complementary color cyan magenta yellow Complementary color= white - color