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• Please bring in a laser pointer for tomorrow’s lab!– Einstein dollars if you do!

What happens to the speed and the wavelength of light as it crosses the boundary in going from air into water?  Speed Wavelength(A) Increases Remains the same(B) Remains the same Decreases (C) Remains the same Remains the same(D) Decreases Increases(E) Decreases Decreases

Quick Whiteboard Review!

Frequency of a wave does not change upon entering a new medium!

The frequency of an EM wave governs how much energy it carries.

Frequency is a property of the wave, and is set once the wave is produced.

Wave speed and wavelength will change in direct proportion upon entering a new medium!

The Doppler Effect also applies to light!

If a source of light is moving toward an observer, the light that the observer receives will have a higher frequency and shorter wavelength than would normally be received!

This is called blueshift. (Light is shifted toward the blue end of the spectrum – higher frequency)

If a source of light is moving away from an observer, the received light will have a lower frequency and longer wavelength than normal!

This is called redshift. (Light is shifted toward the red end of the spectrum – lower frequency)

Double Slit Interference

Thomas Young: The man. The myth.

Conceived and demonstrated the famous and revolutionary double slit experiment in 1802.

First demonstrated the results with water waves in a ripple tank, and then with light waves in a dark room, using a candle and an ingenious apparatus.

Young’s Famous Experiment

Double slitScreen

Flame

Single slit

Coherent LightLight from a source is considered to be coherent if it is

composed of many waves that are in phase with one another.

Light coming from a flame is incoherent light. There are crests and troughs everywhere!

If it is incident upon a thin slit, the light that comes out of the slit will be coherent light. Crests and troughs will be emitted

in phase with one another.

Young’s Famous Experiment

Double slitScreen

Flame

Incoherent light

Single slit

Coherent light

Two sources of coherent light

The results were revolutionary!

Light creates an interference pattern of bright and dark regions on the screen!

The conclusion is inescapable – light is a wave!

Young’s Famous Experiment

Double slitScreen

Flame

Incoherent light

Single slit

Coherent light

Two sources of coherent light

Bright band

Dark band

Bright band

Dark band

Bright band

Two-Source Interference

When two sources of waves are close to one another, they create a beautiful and complex interference pattern.

This can be understood by using the Principle of Superposition!

Principle of Superposition

1)When the crest of one wave meets the crest of another, or the trough of one meets the trough of another, they will constructively interfere and create a large combined wave.

2)When the crest of one wave meets the trough of another, they will destructively interfere, negative one another.

Constructive InterferenceConsider the two in-phase sources of light shown below.

Source 1

Source 2

Point X is a distance L1 away from Source 1, and a distance L2

away from Source 2.

L1

L2 This means that by the time the waves reach X, waves from Source 1 have traveled a distance L1, and waves from Source 2 have traveled a distance L2.

If L1 = L2 …If light wave 1 has undergone a certain number of full oscillations by the time it reaches X…

Then light wave 2 has also undergone the same number of full oscillations by the time it reaches X!

Since the waves were in phase when they were emitted, and traveled the same distance, they will still be in phase when they meet at X!

X will be a bright spot of constructive interference

Source 1

Source 2

Constructive interference will occur if

L1 – L2 = 0

L1 – L2 = λ

(Wave 1 has traveled a full extra wavelength by the time that they meet)

L2 – L1 = λ

(Wave 2 has traveled a full extra wavelength by the time that they meet)

L1 – L2 = 2λ

(Wave 1 has traveled two extra wavelengths by the time that they meet)

L2 – L1 = 2λ

(Wave 2 has traveled two extra wavelengths by the time that they meet)

In general,

L1

L2

Constructive interference (the center of a bright band) will occur if

m = 0 if the waves have traveled the same distance, m = 1 if one of the waves has traveled one extra wavelength, m = 2 if one of the waves have traveled two extra wavelengths, etc.

Slit 1

Slit 2

Constructive interference will occur along all of these lines (where crests from source 1 meet crests from source 2)

The central bright line is the m = 0 line. This means that waves from both sources will have traveled the same

distance by the time that they reach any point on this line.

L1 = L2

m = 0

The lines of constructive interference adjacent to the center line are the m = 1 lines. This means that waves from one of

the sources will have traveled exactly one wavelength further than waves from the other source by the time that

they reach any point on these lines.

m = 1 m = 1

The next lines of constructive interference are the m = 2 lines. This means that waves from one of the sources will have traveled exactly two wavelengths further than waves from the other source by the time that they reach any point

on these lines.

m = 2 m = 2

m = 0

Constructive interference will occur on any of these lines, because they satisfy the condition

m = 1 m = 1

m = 2m = 2

Destructive InterferenceConsider the two in-phase sources of light shown below.

The point X is a distance L1 away from Source 1, and a distance L2

away from Source 2.

L1

L2 This means that by the time the waves reach X, waves from Source 1 have traveled a distance L1, and waves from Source 2 have traveled a distance L2.

Source 1

Source 2

If L1 is exactly one half wavelength less than L2 …

A crest from one wave will meet a trough from the other!

The waves will destructively interfere.

2.5 oscillations

3 oscillations

Source 1

Source 2

Destructive interference (darkness) will occur if

L1 – L2 = λ/2

(Wave 1 has traveled an extra half-wavelength by the time that they meet)

L2 – L1 = λ/2

(Wave 2 has traveled an extra half-wavelength by the time that they meet)

L1 – L2 = 3λ/2

(Wave 1 has traveled an extra 1.5 wavelengths by the time that they meet)

L2 – L1 = 3λ/2

(Wave 2 has traveled an extra 1.5 wavelengths by the time that they meet)

In general,

L1

L2

Destructive interference will occur if

m = 1 if one wave has traveled an extra half-wavelength, m = 2 if one wave has traveled an extra 1.5 wavelengths, etc.

Source 1

Source 2

Destructive interference will occur along these lines (where crests from source 1 meet troughs from source 2)

The first line of destructive interference is m = 1. This means that waves from one source have traveled λ/2 further than waves from the

other source by the time that they reach any point on this line.

m = 1 m = 1

The second line of destructive interference is m = 2. This means that waves from one source have traveled 1.5 λ further than waves from the other source by the time that they reach any point on this line.

m = 2 m = 2

Destructive interference will occur on any of these lines, because they satisfy the condition

m = 1 m = 1

m = 2m = 2

m = 3m = 3

d

screen

Bird’s eye view

L

y

θ

Anatomy of the double-slit interference apparatus

d = spacing between the slitsL = distance from slits to screenθ = angle between central line and line to a point on the screeny = distance between central band and point on the screen

d

screenBird’s eye view

L

yL1

L2

When |L1 – L2| = mλ,y will be a bright spot

When |L1 – L2| = (m-1/2)λ,y will be a dark spot

d

screenL

yL1

L2

Some important assumptions that make life way easier!

L >> d d >> λThe spacing of the slits is tiny compared to L

The wavelength of light is tiny compared to d

Caution!

L >> d d >> λ

The following derivation is based upon the assumptions above, which apply only to light – not to sound!

Sound waves have a much larger wavelength than visible light, and so you cannot use the coming simplifications when dealing with sound interference!

That is all.

d

screenL

yL1

L2

A clever way to simplify things when dealing with light!

θ

θ

θd

Since L >> d, we can approximate that both sources emit light toward the screen in about the same direction

The dark blue line represents the extra distance that waves from the bottom slit need to travel to reach the screen!

A clever way to simplify things when dealing with light!

θ

d

dsinθ

When doing calculations for light wave interference involving small double-slits, we will use the (very accurate) approximation

dsinθ = |L1 – L2|

d is the spacing between the slits

θ is the angle from the central axis to the point on the screen that we are analyzing

d

Net Result!

y

When dsinθ = mλ,y will be a bright spot

When dsinθ = (m-1/2)λ,y will be a dark spot

θ