Fundamental Physics II

Fundamental Physics II

PETROVIETNAM UNIVERSITYFACULTY OF FUNDAMENTAL SCIENCES

Vungtau, 2013

Phamj Hong QuangE-mail: [email protected]

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Chapter 6

Pham Hong Quang Fundamental of Drilling and Production

Interference

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Chapter 6 Interference


1.Superposition and Interference

2. Young’s Two-Slit Experiment3. Interference in Reflected

Waves4.Michelson Interferometer

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6.1 Superposition and Interference


If two waves occupy the same space, their amplitudes add at each point. They may interfere either constructively or destructively.

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Interference is only noticeable if the light sources are monochromatic (so all the light has the same wavelength) and coherent (different sources maintain the same phase relationship over space and time).If this is true, interference will be constructive where the two waves are in phase, and destructive where they are out of phase.

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In this illustration, interference will be constructive where the path lengths differ by an integral number of wavelengths, and destructive where they differ by a half-odd integral number of wavelengths

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6.2 Young’s Two-Slit Experiment


If light consists of particles, the final screen should show two thin stripes, one corresponding to each slit. However, if light is a wave, each slit serves as a new source of “wavelets,” as shown, and the final screen will show the effects of interference. This is called Huygens’s principle.

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As the pattern on the screen shows, the light on the screen has alternating light and dark fringes, corresponding to constructive and destructive interference.The path difference is given by:

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The dark fringes are between the bright fringes; the condition for dark fringes is:

Therefore, the condition for bright fringes (constructive interference) is:

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This diagram illustrates the numbering of the fringes.

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How do we locate the vertical position of the fringes on the screen?

1) L >> d2) d >> λThese tell us that θ is smallTherefore,

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d sin m m = 0,1,2,3... Maximum

Lymtan

sintan

dm

Lym sin

dLmym

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I 4I0 cos2 12

2d

sin

The intensity of light along the screen

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6.3 Interference in Reflected Waves


Reflected waves can interfere due to path length differences, but they can also interfere due to phase changes upon reflection.

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There is no phase change when light reflects from a region with a lower index of refraction.There is a half-wavelength phase change when light reflects from a region with a higher index of refraction, or from a solid surface.There is also no phase change in the refracted wave.

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Assume: n1<n2Condition for constructive interference

2)21(2 nmL

22 / nn Because

)21(2 2 mLn

and θ~ 0

Then

Condition for destructive interference mLn 22

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If take in account θ1, condition for constructive interference

122

222 sin2)21(cos2 nLmLn

Because 2

2

12

2sin1cosn

We get

)21(cos2 22 mLn

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CDs (compact disks) depend on interference for their functioning. The signal is encoded as tiny bumps in the surface, and the reflected laser beam varies in intensity depending on whether it is reflecting from a bump or not.

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6.4 Michelson Interferometer


An interferometer works on the principle of superposition. Michelson designed an interferometer to determine the wavelength of light.

Here are the basic building blocks: • A monochromatic source (emitting light waves)

• a detector• two mirrors • one semitransparent mirror (often called beam splitter)

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)(2 21 LL

)(2 21 LLN

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In order to measure the thickness l of a transparent plate with the index of refraction nInsert the plate in the path of light.The number of wavelength in two paths (forwards and backwards) within the plate is:

n

lN2

The number of wavelength in two paths (forwards and backwards) within the same thickness but in air:

lNair

2 )1(2 nlNN air

23Pham hong Quang 23 PetroVietnam Universityg

Thank you!

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Fundamental Physics II