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Physics 2102 Jonathan Dowling. Lecture 27. Ch. 35: Interference. Christian Huygens 1629-1695. Wave Optics: Huygen’s Principle. All points in a wavefront serve as point sources of spherical secondary waves. After a time t, the new

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lecture 27

Physics 2102

Jonathan Dowling

Lecture 27

Ch. 35: Interference

Christian Huygens

1629-1695

wave optics huygen s principle
Wave Optics: Huygen’s Principle

All points in a wavefront serve as point sources of spherical secondary waves.

After a time t, the new

wavefront will be the tangent to all the resulting spherical waves.

Christian Huygens

1629-1695

reflection and refraction laws from huygen s
Reflection and Refraction Laws from Huygen’s

The light travels more slowly in more dense media:

v=c/n (n=index of refraction)

Snell’s law!

Wavelength:

Frequency:

slide4

Young’s Double Slit Experiment:

Lasers are a recent (1960’s) invention. Before that it was challenging

to demonstrate that light was indeed a wave.

Young created a clever simple experiment in 1801 that clearly demonstrated that light was a wave phenomenon.

He first ran a plane wave through a small slit, which produced a quite coherent spherical wave. He then interposed two slits, which produced two spherical waves that interfered with each other on a screen.

slide5

The Lunatic Fringe:

The waves arriving at the screen from

the two slits will interfere constructively

or destructively depending on the different

length they have travelled.

Maximum fringe at q=0, (central maxima)

other maxima at

Similarly for dark fringes: d sin q= (m+1/2) l

slide6

The Return

Of the Phasor!

Phase Difference

2=360°

=180°

example
Example

Red laser light (l=633nm) goes through two slits 1cm apart, and produces a diffraction pattern on a screen 55cm away. How far apart are the fringes near the center?

If the fringes are near the center, we can use

sin q ~ q, and then

ml=dsinq~dq => q=m/d is the angle for each

maximum (in radians)

Dq= l/d =is the “angular separation”.

The distance between the fringes is then

Dx=LDq=Ll/d=55cmx633nm/1cm=35 mm

For the spacing to be 1mm, we need d~ Ll/1mm=0.35mm

example8

q

Example

In a double slit experiment, we can measure the wavelength of the light if we know the distances between the slits and the angular separation of the fringes.

If the separation between the slits is 0.5mm and the first order maximum of the interference pattern is at an angle of 0.059o from the center of the pattern, what is the wavelength and color of the light used?

d sinq=ml =>

l=0.5mm sin(0.059o)

= 5.15 10-7m=515nm ~ green

example9
Example

A double slit experiment has a screen 120cm away from the slits, which are 0.25cm apart. The slits are illuminated with coherent 600nm light. At what distance above the central maximum is the average intensity on the screen 75% of the maximum?

I/I0=4cos2f/2 ; I/Imax=cos2f/2 =0.75 => f=2cos–1 (0.75)1/2=60o=p/3 rad

f=(2pd/l)sinq => q= sin-1(l/2pd)f=0.0022o=40 mrad (small!)

y=Lq=48mm

radio waves
Radio Waves

Two radio towers, separated by 300 m as shown the figure, broadcast identical signals at the same wavelength.

A radio in the car, which traveling due north, receives the signals. If the car is positioned at the second maximum, what is the wavelength of the signals? Where will the driver find a minimum in reception?

dsinq=ml =>

l= dsinq/2

sin q= 400/(4002+10002)1/2=0.37

l=55.7m

“Dark” fringes: dsinq=(m+1/2)l

sinq=(m+1/2)l/d=2.5x55.7m/300m

=0.464 =>q= 28o

tanq=y/1000m => y=1000m x tan(28o)=525m