Interference

• If light is a wave, it should exhibit wave-like phenomena such as interference and diffraction when several conditions are met.
• Monochromatic Light
• filter or sodium flame
• Coherent Light
• one source becomes two by using two slits as the two sources.
• wavelength of light is small, need small slits (without diffraction this will not work)
• Superposition
• light is composed of electric and magnetic fields which obey superposition.
• Constructive Interference
• path difference = full wavelength
• d = ml
• Destructive Interference
• path difference = odd integer half- wavelength
• d = (m + 1/2)l



• Geometry
• screen-slit distance = L
• slit separation = d
• If L >> d
• rays are approximately parallel and the path difference between the two rays is d sinq
• Constructive Interference
• path difference = full wavelength
• dsinq = ml
• small angle approximation
• sinq is about equal to tanq = y/L
• y = ml L/d (bright spots)
• Destructive Interference
• path difference = odd integer half- wavelength
• dsinq = (m + 1/2)l
• Intensity



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• Thin Film Interference
• "Rainbow of Colors"
• Soap Bubbles
• Oil Slicks
• thickness determines which colors strongly reflected
• varying thickness means different colors will be reflected
• light reflecting at second boundary
• travels greater distance
• the light is incident perpendicular to the surface. It is drawn at an angle so that we can distinguish between the incoming and outgoing light.
• 2t
• but the wavelength also changes
• 2nt
• may undergo phase shift
• n₃ > n₂
• l/2
• n₃ < n₂
• 0



• Constructive



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• Destructive



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