Lecture 25

Electromagnetic Waves-Ch 25Wave Optics—Interference --Ch 17

A B C D F0

1

2

3

4

5

6

7

8

Exam 3 Ave = 73

Problems for Wednesday

• 25: 19, 22, 28, 29, 31• WB 25: 13-18

Electromagnetic Waves

Slide 25-33

Sinusoidal Waves

• Single frequency (single color) and single wavelength, λ.

• TRANSVERSE with B and E perpendicular to the direction of motion.

• In vacuum velocity = c = 3.00 x 108 m/s• Right hand rule relates E, B and direction of

propagation–E = cB

Sinusoidal Waves Continued

• Wave traveling in the +x direction with E polarized along the y-axis, and hence B along the z-axis.

0

0

0 0

( , ) sin 2

( , ) sin 2

y

z

x tE x t E T

x tB x t BT

E cB

Sinusoidal Waves continued

• In vacuum, • wave speed is c = 3.00x108 m/s• λ= wavelength (spatial period)• T = (temporal) period• fλ = c

Intensity

• Intensity—power incident on area A divided by A

• Point Source

20 0

12

PI c EA

24SOURCEPIr

Polarization

• Linear or plane polarization: The electric field oscillates along a straight line, the y-axis in our previous example.

• A polarizer chooses a direction (called the polarizer axis) along which the transmitted E-field oscillates.

• First polarizers reduces intensity by ½

21( ) cos ( )2transmitted incidentI I

Photons

• Light particles: In some experiments, photo-electric effect for example, light acts like a particle.

• Energy carried by each photon

346.63 10photonE hf

h x J s

Checking Understanding

A plane electromagnetic wave has electric and magnetic fields at all points in the plane as noted below. With the fields oriented as shown, the wave is moving

A. into the plane of the paper.B. out of the plane of the paper.C. to the left.D. to the right.E. toward the top of the paper.F. toward the bottom of the paper.

Slide 25-34

Polarization

Slide 25-37

Light passed through a polarizing filter has an intensity of 2.0 W/m2. How should a second polarizing filter be arranged to decrease the intensity to 1.0 W/m2?

Slide 25-38

The Electromagnetic Spectrum

Slide 25-39

Problems

• 25: 19 E = 10 V/m in an electromagnetic wave. What is B?

• 22:

– What is λ, f, and electric field amplitude?• 28: I = 10 W/m2 for a linearly polarized wave.

Intensity through polarizer with b) θ = 300 ?

8( , ) (20 / )sin((6.28 10 ) 2 )yE x t V m x x ft

More Problems

• 29: 25% passes polarizer. Angle of polarizer with respect to electric field?

• 31: Unpolarized light with I = 350 W/m2 – What is I after two polarizers with second axis 350

to axis of first?

• Double-slit interference

• Diffraction gratings

• Thin-film interference

• Single-slit diffraction

• Circular-aperture diffraction

Chapter 17Wave OpticsTopics:

Sample question:The vivid colors of this hummingbird’s feathers have a sheen unlike that of ordinary pigments, and they change subtly depending on the angle at which they’re viewed. How does light interact with the feathers to produce this bright display?

Slide 17-1

Water Waves Spread Out behind a Small Opening

Slide 17-6

Light Waves Also Spread Out Behind a Very Narrow Slit

Slide 17-7

Young’s Double-Slit Interference Experiment

Slide 17-8

Analyzing the Double-Slit Experiment

Slide 17-9

Bright and Dark Fringes in the Double-Slit Experiment

Slide 17-10

Problems 17

• CQ1: frequency in water, glass• CQ3: change in λn , does it change apparent

color?• MC17: what changes when light enters glass?• 1: travel time through piece of glass