1. PHY 228: Optics, Relativity, and Thermal Physics Professor: Joseph Brill, CP381, 7-4670, jwbrill@uky.edujwbrill@uky.edu Class Time: MWF 12, CP222 Office Hours: W, R 10:30-11:30 Course Website: http://www.pa.uky.edu/~brill/PHY228/ Required Text: Physics For Scientists and Engineers (9 th Ed.) Serway and Jewett (Cengage Learning) [webassign and/or hybrid copy and/or hardcopy (8 th or 9 th )] [The webassign website is: https://webassign.net/ ]https://webassign.net/.

2. Optics: The Study of Light Light: an Electromagnetic Wave (propagating oscillations of electric (E) and magnetic (B) fields) But what are Electric and Magnetic Fields?

3. earth Consider the gravitational field (g, ). It points in the direction of the acceleration due to gravity of any mass (m) at that point, and the strength of the field (length of arrow) is proportional to the magnitude of the acceleration. Near a mass M, a grav = g = -GM r /r 2. Since F grav = ma grav = mg g = F grav /m. 

4. Similarly, an electric field (E) surrounds an electric charge (q), with the field pointing away from a positive charge and toward a negative charge. If another charge (Q) is placed in the field, it will feel a force in the direction of E if Q is positive and opposite E if Q is negative: F = QE Note that this implies that like-sign charges repel and opposite-sign charges attract.

5. Two other examples:

6. A magnetic field (B ) surrounds a bar magnet, and points in the direction that a compass needle at each position would point. It can also be mapped by sprinkling iron powder around the magnet.

7. More complicated patterns: The magnetic field is created by spinning electrons (which are “nanoscopic” electric currents) in the bar magnet and interacts with the compass needle or iron filings through their own spinning electrons (“nanoscopic” currents).

8. More fundamentally, a magnetic field surrounds any moving charge (e.g. an electric current) and interacts with any other moving charge (or current): F B = Q v x B Therefore, the total electric and magnetic force on a charge is: F = QE + Q v x B

9. Electric fields (E) surround electrical charges and magnetic fields (B) are created by moving (or spinning) charges (currents). Faraday showed that electric fields can also be created by changing magnetic fields and Maxwell showed that magnetic fields could also be created by changing electric fields. These effects are summarized in “Maxwell’s Equations.” (Eqtns. 34.4-34.7, to be studies in PHY232) Consider a material in which there are no free charges or currents and in which the electric field points in the y-direction but is changing along the x-direction. Then if E y changes in time, it creates a B z, and Maxwell’s Eqtns. reduce to:  E y /  x = -  B z /  t (1)  E y /  t = - (  ) -1  B z /  x (2) (Note that E y and B z are functions of x and t.)  and  are the dielectric constant and magnetic susceptibility of the material, which are measures of how much bound charges and spins in the material can respond to electric and magnetic fields. dielectric material

10.  E y /  x = -  B z /  t (1)  E y /  t = - (  ) -1  B z /  x (2) Differentiate Eqtn. (1) with respect to x:  2 E y /  x 2 = -  (  B z /  t)/  x = -  (  B z /  x)/  t =  2 E y /  t 2 (3) or  2 E y /  t 2 = (  ) -1  2 E y /  x 2 This is just the wave equation (Eqtn. 16.27:  2 y/  t 2 = v 2  2 y/  x 2 ), where  = 1 /v 2, the speed of the wave. The solutions are traveling waves of the form (Eqtn. 16.5): E y = E y0 sin [2π(x  vt)/ ], B z = B z0 sin [2π(x  vt)/ ], can change order of differentiation v

11. E y = E y0 sin [2π(x  vt)/ ], B z = B z0 sin [2π(x  vt)/ ],  E y /  x = -  B z /  t  B z /  t =  (2πv/ ) B z0 cos[2π(x  vt)/ ],  E y /  x = (2π/ ) E y0 cos [2π(x  vt)/ ],  B z0 =  E y0 /v. (The + sign is for a wave traveling toward -x and the minus sign is for a wave traveling toward +x.) is the wavelength of the wave and its frequency is f = v/. v