Announcements 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 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 slit Screen Flame Single slit

Coherent Light Light 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 slit Screen 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 slit Screen 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 Interference Consider the two in-phase sources of light shown below. Source 1 Source 2 Point X is a distance L 1 away from Source 1, and a distance L 2 away from Source 2. L1L1 L2L2 This means that by the time the waves reach X, waves from Source 1 have traveled a distance L 1, and waves from Source 2 have traveled a distance L 2.

If L 1 = L 2 … 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 L 1 – L 2 = 0 L 1 – L 2 = λ (Wave 1 has traveled a full extra wavelength by the time that they meet) L 2 – L 1 = λ (Wave 2 has traveled a full extra wavelength by the time that they meet) L 1 – L 2 = 2λ (Wave 1 has traveled two extra wavelengths by the time that they meet) L 2 – L 1 = 2λ (Wave 2 has traveled two extra wavelengths by the time that they meet)

In general, L1L1 L2L2 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. L 1 = L 2 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

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 = 0 Constructive interference will occur on any of these lines, because they satisfy the condition m = 1 m = 2

Destructive Interference Consider the two in-phase sources of light shown below. The point X is a distance L 1 away from Source 1, and a distance L 2 away from Source 2. L1L1 L2L2 This means that by the time the waves reach X, waves from Source 1 have traveled a distance L 1, and waves from Source 2 have traveled a distance L 2. Source 1 Source 2

If L 1 is exactly one half wavelength less than L 2 … 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 L 1 – L 2 = λ/2 (Wave 1 has traveled an extra half-wavelength by the time that they meet) L 2 – L 1 = λ/2 (Wave 2 has traveled an extra half-wavelength by the time that they meet) L 1 – L 2 = 3λ/2 (Wave 1 has traveled an extra 1.5 wavelengths by the time that they meet) L 2 – L 1 = 3λ/2 (Wave 2 has traveled an extra 1.5 wavelengths by the time that they meet)

In general, L1L1 L2L2 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

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

Destructive interference will occur on any of these lines, because they satisfy the condition m = 1 m = 2 m = 3

d screen Bird’s eye view L y θ Anatomy of the double-slit interference apparatus d = spacing between the slits L = distance from slits to screen θ = angle between central line and line to a point on the screen y = distance between central band and point on the screen

d screen Bird’s eye view L y L1L1 L2L2 When |L 1 – L 2 | = mλ, y will be a bright spot When |L 1 – L 2 | = (m-1/2)λ, y will be a dark spot

d screen L y L1L1 L2L2 Some important assumptions that make life way easier! L >> dd >> λ The spacing of the slits is tiny compared to L The wavelength of light is tiny compared to d

Caution! L >> dd >> 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 screen L y L1L1 L2L2 A clever way to simplify things when dealing with light! θ θ θ d 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 = |L 1 – L 2 | 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