Physics 116 Lecture 21 Wave optics Nov 3, 2011 R. J. Wilkes Email: - - PowerPoint PPT Presentation

• R. J. Wilkes

Email: ph116@u.washington.edu

Physics 116

Lecture 21

Wave optics

Nov 3, 2011

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• Exam 2 next Monday: same procedures as last time
• Practice exam posted Thursday, in class Friday
• YOU bring bubble sheet, pencil, calculator
• Practice questions for Exam #2 are posted (in slides

directory), I will go over solutions in class tomorrow

• Kyle will have special office hour: Monday, 11:30, B442

Announcements

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Today

Lecture Schedule

(up to exam 2)

11/3/11

Quiz: #8

Today, almost all large astronomical telescopes are reflectors, because with a mirror instead of a lens…

A.Since refraction is not involved, there is no color aberration B.There is only one surface to grind and polish, which is easier and cheaper C.Both of the above D.None of the above

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Physical (wave) optics

• So far, we have been using simple ray-tracing methods to

understand behavior of light on a macroscopic scale – Analyze optical systems with diagrams and lens/mirror eqns. – Works as if light were a stream of particles (rays) – Accurate for system lengths from cm up to size of Universe

• On a microscopic scale (few mm down to wavelength of light),

ray optics does not work: must employ the wave nature of light – Take into account the physical properties of waves: superposition and interference effects

• We’ve already discussed this: brief review follows

– Wave optics applies to behavior of light in and around

• Narrow apertures (mm or smaller)
• Arrays of apertures (gratings, meshes, screens)
• Edges of barriers (if we look closely enough)
• Reflections in thin (few wavelengths thick) films

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Interference patterns

• Imagine two kids paddling their hands in a pond in unison
• Waves (ripples) propagate outward, and overlap
• There will be lines of reinforcement, and lines of cancellation

(constructive and destructive interference)

Halfway between are lines of destructive interference lines of reinforcement, where peaks overlap (constructive interference)

From mid-October:

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Interference = defining property of waves

• If you see interference effects, you are looking at waves !

Case study: Isaac Newton thought light was a stream of particles Newton’s “Opticks” (1687) explained all observations at the time Thomas Young (120 years later) observed interference effects with light Only waves could do that… Wave theory of light replaced Newton’s

• Interference depends on phase relationship of overlapping waves
• Phase relationship depends on distance from source

Recall: Phase at distance D from source = 2! (D/") but sin/cos repeat every cycle, so all that matters is where we are relative to start of latest cycle: fraction of a cycle Phase at distance D from source = 2! [ fractional part of (D/") ] Example: fractional part of 5.678 is 0.678 From mid-October: Important point to review:

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Phase relationships

Example: source of sound has "=1.5m Point A is 2.5 m away, B is 5.5 m away, C is 7 m away Phase values are

D / " (distance, in units of wavelengths)

A B C A, B, C are all 2/3 along a cycle, so sound waves have the same phase at all these points From mid-October: To make this acoustic example describe light waves, just change wavelength units from meters to nanometers!

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Example: 2 sound sources with same f

A B C

Point A: sources 1 and 2 are in phase, so we get constructive interference Points B and C: 1 and 2 are “180 deg out of phase”, so destructive interference

1 2 From mid-October: Solid line: R = one wavelength, dashed line: R= wavelength

light

These could be closely spaced pinholes in an

• paque screen

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• Instead of loudspeakers, let’s consider radio antennas

– spaced 3 km apart, in phase: same electrical signal goes to both Observer 4km away, parallel to antenna 1, finds constructive interference (signal is double intensity of a single antenna’s) What f is being transmitted? This is just the lowest possible frequency to give constructive interference. Any integer multiple (harmonic) of this f will also produce constructive interference at the observer’s location: then n > 1 Notice: this is just the stereo loudspeaker example, with meters changed to km and speed of sound in air changed to speed of light 1 2

3km 4km 5km

D1 = 4km D2 = 3km

( )

2 + 4km

( )

2 = 5km

D2 D1 = n for n = 1, = D2 D1 = 1km f = c = 300,000 km / s 1km = 300kHz

Another example reworked:

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Coherence

• One big difference between acoustics and optics: ordinary light sources

have billions of independent radiators – In acoustics, we only discussed simple cases of one source (or 2 sources “in phase”) – Light bulb = 1023 tungsten atoms, each emitting light on its own schedule!

• Incoherent light source: jumble of wavelengths and phases

– To have constant phase relationships, to observe interference effects, we need to either

• View a tiny part of an incoherent source (use slits, pinholes)
• Have a source of coherent light (all atoms emit in synchrony)

– Simple to do today: use a laser – This option did not exist until 1960s !

Broad spectrum

• f wavelengths

mixed together Monochromatic (only 1 wavelength is produced) 11/3/11 11

• We see interference effects when waves overlap (superposition) after

travelling different paths from their source

• For EM waves that are coherent (phase relationship at their source is

fixed, and does not vary with time)

– Constructive interference if path difference is zero or an integer number of wavelengths – Destructive interference if path difference is an odd integer number of half-wavelengths 1 2

• bserver

l1 l2

Constructive if: 2 1 = m m = 0,1,2… and Destructive if: 2 1 = m 1 2

• m = 1,2,3…

alternative statement: 2 1 = n 2

• n = 1,3,5…
• Constructive vs destructive interference

(For phase relationships between these extremes, we get intermediate intensities)

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(Even number of half-wavelengths = integer number of full wavelengths)

Young’s 2-slit experiment

Some call it the most important experiment in physics

– Fundamental impact on quantum theory – as we shall see…

• Make a mask with 2 pinholes or narrow slits, closely spaced

– What’s “narrow”? What’s “close”?

• On the scale of visible light wavelength: fraction of mm
• Illuminate with plane waves (optical equivalent of equally spaced

water waves at a beach, with all wave peaks parallel) – How do we get plane waves of visible light? Use a laser – How did Thomas Young manage in 1804?

www.physics2000.com/

plane waves

2-slit interference pattern in laser light

• Used a pinhole to view a tiny patch of lamp surface
• “Partially coherent light” – pattern is partially

washed out

• The waves interfere to form bright and dark fringes
• n a viewing screen some distance away

We can simulate this with water waves in a tank Slits = barrier with 2 holes

Contemporary of Newton, advocate of wave theory of light Proposed a mechanism for wave propagation:

• Each point on a light wavefront acts like a point source of light

– Produces expanding spherical wavelets – Superposition of wavelets from all points on original wavefront produces the next wavefront – Repeat…

Huygens’ principle

Christiaan Huygens (English pronunciation: /hanz/), Dutch, 1629 – 1695

spherical wavelets plane wave

Today, Maxwell’s equations tell us how EM waves propagate, but Huygens’ Principle provides a handy model to help us picture interference phenomena.

Picture shows wavelets from 3 points – imagine every point adding in its contribution:

• Illuminate a pinhole or slit with light from a distant, coherent source

– Nearby source would give spherical waves, distant source = plane waves – Coherent = from a laser*, or by using another pinhole to restrict area of light source used

• Place a mask with 2 slits in the beam of light

– Slit spacing d should be “small” (not many wavelengths)

• Place a screen far away (many wavelengths)

– Rays* from each slit are nearly parallel when they arrive

• We get a bright fringe on screen parallel to midpoint

– Central bright fringe – equal path lengths from the 2 slits – Constructive interference

• Where is the next bright fringe?

– At what angle do we get next constructive interference? – Path difference from the 2 slits must be 1 or more wavelengths

2-slit experiment in detail

* We’ll talk about ‘rays’ only to get path lengths – then we’ll compare to wavelengths * Lasers supply plane waves at any distance = 0 =

• Calculate the angle to the next bright fringe:

– Central fringe for m=1, the next bright fringe on either side for +1, etc – Dark fringes = destructive interference:

2-slit experiment in detail

2 1 = d sin Constructive if d sin = m, m = 0, ±1, ± 2, ± 3… 1 2

l1 l2

(angle to next bright fringe)

• Slit mask

Ray to slit midpoint Ray to slit midpoint Ray to next bright fringe Ray to next bright fringe 90 d sin d

On this scale, the screen is miles away…

= 0 =

= m 1 2

• m = ±1, ± 2, ± 3…