IVA. Electromagnetic Waves and Optics1. Basic properties of electromagnetic waves

cEB /

Note: 1 nanometer = 10-9 meter

smc /1031 8

00

f

cSpeed of light: Wave length:

For electromagnetic waves:

Electromagnetic waves are transverse waves

E

v

B

1

2. Polarization(Polarizeation of transverse waves)

2.1 Waves on string (polarization and polrizing filters)

2

2.2 Electromagnetic waves (polarized light)

z

direction of wave motion

E

B

x

y

Electromagnetic waves are transverse waves

This wave is polarized in y direction

Light is polarized when its electric fields oscillate in a single plane, rather than in any direction perpendicular to the direction of propagation.

E

v

B

The relation between directions of electric field E magnetic field B and electromagnetic wave velocity v is given by the right hand rule: rotation from E to B gives v.

Example: An electromagnetic wave in vacuum is moving in +y direction. At time t=0 and at position (x,y,z)=(0,0,0), the electric field is pointing in the +z direction. In what direction is pointing the magnetic field at that time and position?

E

v

B

y

z

x

3

2.3 Unpolarized light

(a)Unpolarized light consist of waves with randomly directed electric fields. Here the waves are all traveling along the same axis, directly out of the page, and all have the same amplitude E.

(b)A second way of representing unpolarized light – the light is the superposition of two polarized waves whose planes of oscillation are perpendicular to each other.

021 II 0I - intensity of unpolarized light

I - intensity of polarized component

4

Example (two sheets):

•Polarized light will not be transmitted through a polarized film whose axis is perpendicular to the polarization direction.

•This means that if initially unpolarized light passes through crossed polarizers, no light will get through the second one.

2.4 Polarizing sheets

5

Example (two sheets):•The light transmitted by polarizing sheet P1 is vertically polarized, as represented by the vertical double arrow. •The amount of that light that is transmitted by polarizing sheet P2 depends an the angle between the polarization direction of that light and the polarizing direction of P2

6

Question: What happened when light passes through a polarizer?

Answer: Only the component parallel to the polarization axis is transmitted.

Becouse of that: If the incoming light is plane-polarized (and has intensity I0),

the outgoing intensity is:

2.5 Malus’s law

2~ EI

7

Example (three sheets):

03

0323

2432

23

081

1412

12

021

1

094.0

30cos

60cos

II

IIII

IIII

II

8

3. Interference (review)Interference – combination of waves (an interaction of two or more waves arriving at the same place)Important: principle of superposition

(a) If the interfering waves add up so that they reinforce each other, the total

wave is larger; this is called “constructive interference”.

(b) If the interfering waves add up so that they cancel each other, the total

wave is smaller (or even zero); this is called “destructive interference”.

Valley

Valley Peak

(a)(b)

(a)Waves source No shift or shift by

(b)

Shift by

,...2,1,012

m

mrr 21

12 mrr

9

3.1 Young’s experiment (Double-Slit Interference)

Depending on the path length difference between the slits and the screen, the wave can interfere constructively (bright spot) or destructively (dark spot).

sind

,..2,1,0

edestructiv - sin

veconstructi - sin

21

m

md

md

m

m

x

edestructiv -

veconstructi -

sintan

21

d

mxy

d

mxy

xxy

m

m

mmm

m

intensity

10

Example: In a double-slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0 cm. What happens to the distance between adjacent maxima when the slit separation is cut in half?

A) It increases to 2.0 cm B) It increases to 4.0 cm C) It decreases to 0.50 cm D) It decreases to 0.25 cm

Example: Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes on a screen 5.00 m away are 6.5 cm apart near the center of the pattern. What is the wavelength of the light?

?

5.6

00.5

048.0

1

cmy

mx

mmdveconstructi -

d

mxym

1

R

yd

nmmm

m 62410.624 5.00m

105.610048.0 9

23

11

Dispersion in Young’s experiment

Since the position of the maxima (except the central one) depends on wavelength, fringes (except the central one) contain a spectrum of colors

Question: The separation between adjacent maxima in a double-slit interference pattern using monochromatic light is

A) greatest for red light B) greatest for green light C) greatest for blue light D) the same for all colors of light

12

The waves spread out from

the opening!

3.2 DiffractionWhat it is? The bending of waves behind obstacles or apertures into the ”shadow region”, that can be considered as interference of many waves.

Haw to observe?Diffraction is most pronounced when the wavelength of the wave is similar to the size of the obstacle or aperture. For example, the diffraction of sound waves is commonly observed because the wavelength of sound is similar to the size of doors, etc.

•Light will diffract around a single slit or obstacle.•The resulting pattern of light and dark stripes on a screen is called a diffraction pattern (fringes).

•This pattern arises because different points along a slit create wavelets that interfere with each other just as a double slit would.

13

Example: In order to obtain a good single slit diffraction pattern, the slit width could be:A) /100 B) /10 C) D) 10 E)100

Diffraction from a single slit (intensity)

Minima (dark fringes):

,...3,2,1

sin

m

mD m

14

Example: Light of wavelength 610 nm is incident on a slit 0.20 mm wide and the diffraction pattern is produced on a screen that is 1.5 m from the slit. What is the width of the central maximum?

mmmmy

D

mxy

2.91510.91020.0

106105.122 3

3

9

?2

5.1

20.0

610

y

mx

mmD

nm

Example: Light of wavelength 687 nm is incident on a single slit 0.75 mm wide. At what distance from the slit should a screen be placed if the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the screen?

mmm

mmx

m

yDx

D

mxy

93.0687.02

75.07.1

106872

1075.0107.1

9

33

?

7.1

75.0

687

x

mmy

mmD

nm

15