Lectures on interference

# Lectures on interference - Wave Optics Wave optics is a...

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Wave Optics • Wave optics is a study concerned with phenomena that cannot be adequately explained by geometric (ray) optics • These phenomena include: – Interference Notes – Diffraction – Polarization Interference of light passing through a soap film

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Interference • Similar to mechanical waves, when multiple light waves are present, the resultant wave is a sum of these waves • In constructive interference the amplitude of the resultant wave is greater than that of either individual wave In destructive interference the amplitude of the resultant Notes wave is less than that of either individual wave • All interference associated with light waves arises when the electromagnetic fields that constitute the individual waves combine
Conditions for Interference • No interference of waves observed from two light bulbs • This is because light waves arriving to observer from the bulbs have phases that randomly change in time • To observe interference of light waves, the following two observer Notes conditions must be met: 1) The sources must be coherent • They must maintain a constant phase with respect to each other 2) The sources should be monochromatic • Monochromatic means they have a single wavelength

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Producing Coherent Monochromatic Sources of Light • Lasers produce coherent monochromatic sources of light (need to learn quantum mechanics to understand lasers) • One can use a prism and a narrow slit to make a monochromatic source of light Notes
Review: Superposition of Sinusoidal Waves • Assume two sinusoidal waves. • The waves differ in phase: y 1 = A sin (k x – ω ω ω ω t + φ 1 ) y 2 = A sin ( k x t + 2 ) • The resultant wave is given by: Notes y = y 1 +y 2 = 2A cos (( ) ) ) /2) sin (k x – t + ( ) ) ) /2) Note that only phase constant difference is important for the interference pattern. If both phase constant change by the same value, the interference pattern does not change

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Producing Coherent Sources • There are tricks (based on the fact that interference depends only on (( φ 1 2 ) ) by which you can use one incoherent source of light to produce two coherent sources of light. • Example: light from a monochromatic source is used to illuminate a barrier • The barrier contains two narrow slits Notes – The slits are small openings • The light wave emerging from the two slits are coherent with respect to each other since a single source produces the original light beam and thus random changes of phase of light will not affect the interference pattern
Diffraction • From Huygens’s principle we know the waves spread out from the slits • This divergence of light from its initial

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Lectures on interference - Wave Optics Wave optics is a...

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