Physics 102: Lecture 20, Slide 1

Physics 102: Lecture 20Interference

Physics 102: Lecture 20, Slide 2

Phys 102 recent lectures

• Lecture 14 – EM waves

• Lecture 15 – Polarization

• Lecture 20 & 21 – Interference & diffraction

• Lecture 16 – Reflection

• Lecture 17 – Spherical mirrors & refraction

• Lecture 18 – Refraction & lenses

• Lecture 19 – Lenses & your eye

Light as a wave

Light as a ray

Physics 102: Lecture 20, Slide 3

Superposition

t

+1

-1

t

+1

-1

t

+2

-2

+

Constructive Interference

In Phase

Physics 102: Lecture 20, Slide 4

Superposition

t

+1

-1

t

+1

-1

t

+2

-2

+

Destructive Interference

Out of Phase

180 degrees

Physics 102: Lecture 20, Slide 5

ACT: Superposition

+Different f

1) Constructive 2) Destructive 3) Neither

-1.5

-1

-0.5

0

0.5

1

1.5

-1.5

-1

-0.5

0

0.5

1

1.5

Physics 102: Lecture 20, Slide 6

Interference Requirements

• Need two (or more) waves

• Must have same frequency• Must be coherent (i.e. waves must have definite

phase relation)

Physics 102: Lecture 20, Slide 7

Demo: Interference for Sound …For example, a pair of speakers, driven in phase, producing a tone of a single f and :

l1 l2

But this won’t work for light--can’t get coherent sources

hmmm… I’m just far enough away that l2-l1=/2, and I hear no sound at all!

Physics 102: Lecture 20, Slide 8

Interference for Light …

• Can’t produce coherent light from separate sources. (f 1014 Hz)

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

Today’s lecture

Next lecture

Physics 102: Lecture 20, Slide 9

Young’s double slit/rays

Bright spots

Shadow

This is not what is actually seen!

Monochromatic light travels through 2 slits onto a screenWhat pattern emerges on the screen?

Physics 102: Lecture 20, Slide 10

•

•

Young’s double slit/HuygensRecall Huygens’ principle: Every point on a wave front acts as a source of tiny wavelets that move forward.

Wave crests in phase = constructive interference

Bright and dark spots on screen!

Constructive = bright

Destructive = dark

Physics 102: Lecture 20, Slide 11

•

•

Young’s double slit: Key idea

Key for interference is this small extra distance.

Consider two rays traveling at an angle :

θ

Bottom ray travels a little further (2 in this case)

Physics 102: Lecture 20, Slide 12

Young’s double slit: Quantitative

Constructive: dsin() = mDestructive: dsin() = (m+1/2)

Consider two rays traveling at an angle Assume screen is very far away (L>>d):

θ ≈≈

≈L

Path length difference = dsin()

θ

where m = 0, 1, 2

m = +2

Need < d

Physics 102: Lecture 20, Slide 13

Young’s double slit: Quantitative

Constructive: dsin() = mDestructive: dsin() = (m+1/2)

Assume screen is very far away (L>>d), angles are small:

θ

Ldsin()

θ

m = 0, 1, 2

m = 0

m = +1

m = -1

m = -2

m = +2

y

sin() tan() = y/L

y ≈ mL/d

y ≈ (m+1/2)L/d

Physics 102: Lecture 20, Slide 16

ACT: Preflight 20.3

1) increases 2) same 3) decreases

θ

Ldsin()

θ m = 0

m = +1

m = -1

m = -2

m = +2

y

When this Young’s double slit experiment is placed under water, the separation y between minima and maxima:

Physics 102: Lecture 20, Slide 17

Preflight 20.2In the Young 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

Physics 102: Lecture 20, Slide 18

Thin Film Interference

n1 (thin film)

n2

n0=1.0 (air)

t

1 2

Get two waves by reflection off two different interfaces: interference!

Ray 2 travels approximately 2t further than ray 1.

Light is incident normal to a thin film

Note: angles exaggerated for clarity

Physics 102: Lecture 20, Slide 19

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 – 180º phase change upon reflection (shift by /2)

Incident

Reflected

n1

n2

Refracted

Incident

Reflected

Refracted

Physics 102: Lecture 20, Slide 20

Thin Film Summary

n1 (thin film) n2

n = 1.0 (air)

t

1 2

Ray 1: 1 = 0 or ½

Determine , number of extra wavelengths for each ray.

If |2 – 1| = ½ , 1 ½, 2 ½ …. (m + ½) destructive

If |2 – 1| = 0, 1, 2, 3 …. (m) constructive

Note: this is wavelength in

film! (film= o/n1)

+ 2 t/ film

Reflection Distance

Ray 2: 2 = 0 or ½+ 0

This is important!

Physics 102: Lecture 20, Slide 21

ACT: Thin Film Practice

n1 (thin film) n2

n = 1.0 (air)

t

1 2

Blue light (0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of water (n2 = 1.3).

A) 1 = 0 B) 1 = ½ C) 1 = 1

What is 1, the total phase shift for ray 1

Physics 102: Lecture 20, Slide 22

Is the interference constructive or destructive or neither?

Thin Film Practice

n1 (thin film) n2

n = 1.0 (air)

t

1 2

Blue light (0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of water (n2 = 1.3).

1 =

2 =

Phase shift = |2 – 1| =

Physics 102: Lecture 20, Slide 23

ACT: Thin Film Practice II

n1 (thin film) n2

n = 1.0 (air)

t

1 2

Blue light (0 = 500 nm) incident on a glass (n1 = 1.5) cover slip (t = 167 nm) floating on top of plastic (n2 = 1.8).

1 =

2 =

Phase shift = |2 – 1| =

Is the interference : 1) constructive 2) destructive 3) neither?