The interference of light

Transcription

1 The interference of light For a long time there was a dispute about what light was. Was it made up of particles, or waves? In 1801, Thomas Young carried out a famous experiment (Young s double slit) that showed very clearly that light acted as a wave. For now, we ll focus on wave properties of light.

2 Producing a stable interference pattern To produce a stable and clear interference pattern from two sources, the sources should be coherent (maintaining a fixed phase relationship) and monochromatic (having a single wavelength). Two speakers connected to the same source of sound satisfy these criteria. Two light bulbs do not. Two lasers do not. One laser shining on two slits works, though.

3 Conditions for interference For two sources sending out identical waves in phase: Condition for constructive interference path-length difference: L= mλ, where m is an integer Condition for destructive interference path-length difference: L= ( m+ 1/ 2) λ, where m is an integer

4 Understanding the interference pattern The source positions are shown in red. The waves spread out as rings from the sources, red for peaks and blue for troughs. Left source only Right source only Both sources

5 Understanding the interference pattern At any point on the perpendicular bisector to the line joining the sources (like the yellow point) we get constructive interference the path-length difference is zero. 2.5 λ 2.5 λ Left source only Both sources Right source only

6 Both sources Understanding the interference pattern The blue point is half a wavelength farther from the left source than from the right source giving destructive interference at that point. 2.5 λ Left source only 2 λ Right source only

7 Both sources Understanding the interference pattern The purple point is a full wavelength farther from the left source than from the right source giving constructive interference at that point. 3 λ Left source only 2 λ Right source only

8 The double-source equation Let s call the distance between the sources d (usually several wavelengths). For a point a long way from the sources, the path-length difference is d sinθ, where θ is the angle between the perpendicular bisector and the line joining the point to the spot halfway between the sources.

9 The double-source equation For two sources sending out identical waves in phase: Condition for constructive interference dsin θ = mλ, where m is an integer Condition for destructive interference d θ m λ m sin = ( + 1/ 2), where is an integer

10 Changing the wavelength If the wavelength is decreased, what happens to the lines of constructive and destructive interference in the pattern? 1. They get farther apart 2. They get closer together 3. They stay the same

11 Changing the wavelength sin θ = m d λ Decreasing the wavelength decreases the angles at which constructive and destructive interference happens, so the lines in the pattern get closer together.

12 Changing d If the distance between the sources is decreased, what happens to the lines of constructive and destructive interference in the pattern? Remember d sin(θ) = mλ 1. They get farther apart 2. They get closer together 3. They stay the same

13 Changing d sin θ = m d λ Decreasing d increases the angles at which constructive and destructive interference happens, so the lines in the pattern get farther apart.

14 Adding sources What happens to the interference pattern when we add more sources? Let's start by switching from two sources d apart to three sources d apart. Do we still get maxima at the same angles where we got maxima for two sources? 1. Yes 2. No

15 Adding sources Yes, the constructive interference equation applies for any number of sources separated by a distance d : d sin(θ) = mλ. Now we're simply adding three waves in phase instead of two, and for N sources we'd add N waves in phase.

16 Adding sources, II What happens to the interference pattern when we add more sources? Let's start by switching from two sources d apart to three sources d apart. Do we still get minima at the same angles where we got minima for two sources? 1. Yes 2. No

17 Adding sources, II No! We got destructive interference when the pathlength difference is half a wavelength because the first two waves canceled. They still cancel, so there is nothing to cancel the third wave. To get three waves to cancel, the path-length difference is one-third or two-thirds of a wavelength, not half a wavelength.

18 Adding slits For light, adding sources really means adding slits (openings) for the laser light to pass through each slit acts as a source. By adding more slits, the interference maxima are much brighter, and a lot sharper.