textbook sections 28-1 -- 28-3 physics 1161: lecture 20 interference

• textbook sections 28-1 -- 28-3

Physics 1161: Lecture 20Interference

Superposition

t

+1

-1

t

+1

-1

t

+2

-2

+

Constructive Interference

In Phase

Superposition

t

+1

-1

t

+1

-1

t

+2

-2

+

Destructive Interference

Out of Phase

180 degrees

Which type of interference results from the superposition of the two waveforms shown?

1 2 3

0% 0%0%

1. Constructive2. Destructive3. Neither+

Different f

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5

-1

-0.5

0

0.5

1

1.5

Which type of interference results from the superposition of the two waveforms shown?

1 2 3

0% 0%0%

1. Constructive2. Destructive3. Neither+

Different f

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5

-1

-0.5

0

0.5

1

1.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Interference for Light …• Can’t produce coherent light from separate

sources. (f 1014 Hz)

Single source

Two different paths

Interference possible here

• Need two waves from single source taking two different paths– Two slits– Reflection (thin films)– Diffraction*

Coherent & Incoherent Light

Double Slit Interference Applets

• http://www.walter-fendt.de/ph14e/doubleslit.htm

• http://vsg.quasihome.com/interfer.htm

http://www.walter-fendt.de/ph14e/doubleslit.htm

http://www.walter-fendt.de/ph14e/doubleslit.htm

http://vsg.quasihome.com/interfer.htm

Young’s Double Slit Applet

http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/PhysicsInitiative/Physics2000/applets/twoslitsa.html




Young’s Double Slit Layout

Interference - Wavelength

Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be:

1 2 3

0% 0%0%

1. Constructive2. Destructive3. It depends on L

Screen a distance L from slits

Single source of monochromatic light

d

2 slits-separated by d

L

Light waves from a single source travel through 2 slits before meeting at the point shown on the screen. The interference will be:

1 2 3

0% 0%0%

1. Constructive2. Destructive3. It depends on L



d


L

The rays start in phase, and travel the same distance, so they will arrive in phase.

Young’s Double SlitCheckpoint



d


1) The pattern of maxima and minima is the same for original and modified experiments.

2) Maxima and minima for the unmodified experiment now become minima and maxima for the modified experiment.

L

½ l shift

The experiment is modified so that one of the waves has its phase shifted by ½ l. Now, the interference will be:




d


1) The pattern of maxima and minima is the same for original and modified experiments.

2) Maxima and minima for the unmodified experiment now become minima and maxima for the modified experiment.

L

½ l shift

The experiment is modified so that one of the waves has its phase shifted by ½ l. Now, the interference will be:

For example at the point shown, he rays start out of phase and travel the same distance, so they will arrive out of phase.

Young’s Double Slit Concept



d


L

At points where the difference in path length is 0, l,2l, …, the screen is bright. (constructive)

At points where the difference in path

length is

the screen is dark. (destructive)

2

5 ,

23 ,

2

Young’s Double Slit Key IdeaL

Two rays travel almost exactly the same distance. (screen must be very far away: L >> d)

Bottom ray travels a little further.

Key for interference is this small extra distance.

d

Path length difference =

d

Young’s Double Slit Quantitative

Destructive interference dsin (m

12)

Constructive interference dsin m

where m = 0, or 1, or 2, ...

d sin q

Need l < d

d

Destructive interference dsin (m

12)

Constructive interference dsin m

where m = 0, or 1, or 2, ...

Young’s Double Slit Quantitative

y

sin(q) tan(q) = y/L

dLm

y

d

Lmy

21

L

A little geometry…

Young’s Double Slit Under WaterCheckpoint

d

L

y

When this Young’s double slit experiment is placed under water, how does the pattern of minima and maxima change?

1) the pattern stays the same

2) the maxima and minima occur at smaller angles

3) the maxima and minima occur at larger angles

Young’s Double Slit Under WaterCheckpoint

d

L

y

When this Young’s double slit experiment is placed under water, how does the pattern of minima and maxima change?

1) the pattern stays the same

2) the maxima and minima occur at smaller angles

3) the maxima and minima occur at larger angles

…wavelength is shorter under water.


In Young’s double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light?

1) Yes 2) No

Young’s Double Slit CheckpointIn Young’s double slit experiment, is it possible to see interference maxima when the distance between slits is smaller than the wavelength of light?

1) Yes 2) No

Need: d sin = m l => sin = m l / d

If l > d then l / d > 1

so sin > 1

Not possible!

Reflections at Boundaries

Free End ReflectionNo phase change

Slow Mediumto

Fast Medium

Fast Mediumto

Slow Medium

Fixed End Reflection180o phase change

Newton’s Rings

Iridescence

Soap Film Interference• This soap film varies in

thickness and produces a rainbow of colors.

• The top part is so thin it looks black.

• All colors destructively interfere there.

Thin Film Interference

n1 (thin film)

n2

n0=1.0 (air)

t

1 2

Get two waves by reflection from the two different interfaces.

Ray 2 travels approximately 2t further than ray 1.

Reflection + Phase Shifts

n1

n2

Upon reflection from a boundary between two transparent materials, the phase of the reflected light may change.

• If n1 > n2 - no phase change upon reflection.

• If n1 < n2 - phase change of 180º upon reflection. (equivalent to the wave shifting by l/2.)

Incident wave Reflected wave

Thin Film Summary

n1 (thin film)

n2

n = 1.0 (air)

t

1 2

Ray 1: d1 = 0 or ½

Determine ,d number of extra wavelengths for each ray.

If |(d2 – d1)| = ½ , 1 ½, 2 ½ …. (m + ½) destructiveIf |(d2 – d1)| = 0, 1, 2, 3 …. (m) constructive

Note: this is wavelength in film!

(lfilm= lo/n1)+ 2 t/ lfilm

Reflection Distance

Ray 2: d2 = 0 or ½

This is important!

Thin Film Practice

nglass = 1.5

nwater= 1.3

n = 1.0 (air)

t

1 2

d1 =

d2 =

Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3).

Is the interference constructive or destructive or neither?

Phase shift = d2 – d1 =

Thin Film Practice

nglass = 1.5

nwater= 1.3

n = 1.0 (air)

t

1 2

d1 = ½

d2 = 0 + 2t / lglass = 2t nglass/ l0= 1

Blue light (lo = 500 nm) incident on a glass (nglass = 1.5) cover slip (t = 167 nm) floating on top of water (nwater = 1.3).

Is the interference constructive or destructive or neither?

Phase shift = d2 – d1 = ½ wavelength

Reflection at air-film interface only

Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is:

1 2 3

0% 0%0%

nglass =1.5

nplastic=1.8

n=1 (air)

t

21

1. Constructive2. Destructive3. Neither

Blue light l = 500 nm incident on a thin film (t = 167 nm) of glass on top of plastic. The interference is:

1 2 3

0% 0%0%

nglass =1.5

nplastic=1.8

n=1 (air)

t

21

1. Constructive2. Destructive3. Neither

d1 = ½ d2 = ½ + 2t / lglass = ½ + 2t nglass/ l0= ½ + 1

Phase shift = d2 – d1 = 1 wavelength

Thin FilmsCheckpoint

The gas looks: • bright • dark

A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength…

t = l

nwater=1.3

ngas=1.20

nair=1.0

noil=1.45

The oil looks: • bright • dark

Thin FilmsCheckpoint

The gas looks: • bright• dark

A thin film of gasoline (ngas=1.20) and a thin film of oil (noil=1.45) are floating on water (nwater=1.33). When the thickness of the two films is exactly one wavelength…

t = l

nwater=1.3

ngas=1.20

nair=1.0

noil=1.45

d1,gas = ½

The oil looks: • bright• dark

d2,gas = ½ + 2 d1,oil = ½ d2,oil = 2| d2,gas – d1,gas | = 2 | d2,oil – d1,oil | = 3/2

constructive destructive

textbook sections 28-1 -- 28-3 physics 1161: lecture 20 interference

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