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Interference Physics 202 Professor Lee Carkner Lecture 24

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Interference Due to a phase difference between the incoming waves the amplitude of the resultant wave can be larger or smaller than the original Light can experience such interference as well The interference of light demonstrates the wave nature of light

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The Wave Nature of Light Example: why does refraction occur? A wavefront produces spherical wavelets which propagate outward to define a new wavefront

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Huygen’s Principle

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Refraction and Waves In a vacuum each subsequent wavefront is parallel to the last As a wavefront enters a medium with a larger index of refraction part of the wavefront is in the new medium and part is out Some wavelets lag behind others so the new wavefront is bent If you consider a ray perpendicular to the wavefronts, it is also bent

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Huygen and Snell

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Snell’s Law n = c/v v is the velocity in the medium sin 1 / sin 2 = v 1 / v 2 sin 1 /sin 2 = n 2 /n 1 Which is Snell’s Law: n 1 sin 1 = n 2 sin 2

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Velocity and Wavelength Its velocity is equal to c only in vacuum Light also changes wavelength in a new medium If the new n is larger, v is smaller and so is smaller Frequency stays the same

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Phase Change If light travels through a medium of length L with index of refraction n, the number of wavelengths in that medium is: Consider two light rays that travel the same distance, L, through two different mediums N 2 - N 1 = (L/ )(n 2 -n 1 )

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Phase We can represent phase in different ways Phase differences are seen as brightness variations Constructive interference Destructive interference Intermediate interferences produces intermediate brightness

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Different n’s

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Diffraction When a planar wavefront passes through a slit the wavefront flares out Diffraction can be produced by any sharp edge e.g. a circular aperture or a thin edge

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Diffraction

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Diffraction of a Telescopic Image of the Pleiades

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Basic Interference Interference was first demonstrated by Thomas Young in 1801 The slits produce two curved wavefronts traveling towards a screen The interference patterns appear on the screen and show bright and dark maxima and minima, or fringes

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Interference

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Interference Patterns The two rays travel different distances and so will be in or out of phase depending on if the difference is a multiple of 1 or an odd multiple of 0.5 wavelengths L = What is the path length difference ( L) for a given set-up?

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Path Length Difference Consider a double slit system where d is the distance between the slits and is the angle between the normal and the point on the screen we are interested in L = d sin This is strictly true only when the distance to the screen D is much larger than d

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Path Length

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Maxima and Minima d sin = m For minima (dark spots) the path length must be equal to a odd multiple of half wavelengths: d sin = (m+½)

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Location of Fringes You can locate the position of specific fringes if you know the value of m (called the order) For example: m=1 Zeroth order maxima is straight in front of the slits and order numbers increase to each side

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Interference Patterns You can also find the location of maxima in terms of the linear distance from the center of the interference pattern (y): For small angles (or large D) tan = sin y = m D/d The same equation holds for for minima if you replace m with (m+½)

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Wavelength of Light Young first did this in 1801, finding the average wavelength of visible sunlight The measurement is hard to make because is small

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Coherence Light sources that have a constant phase difference are called coherent Any two random rays from a laser will be in phase The phase difference varies randomly We have assumed coherence in our derivation

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