Interference and Diffraction

Combining Light Waves Interference – the combining of waves via the superposition principle Add the amplitudes (displacements) Combined wave is called the resultant wave Interference only takes place when waves have the same wavelength Constructive interference – resultant amplitude is greater than component amplitudes Destructive interference – resultant amplitude is less than the greatest component amplitude Component amplitudes at least partially cancel each other out

Combining Light Waves Waves must have a constant phase difference to be observed Phase difference – how the waves overlap Crest-to-crest is 0° – in phase Crest-to-trough is 180° – out of phase Coherence – the correlation between the phases of two or more waves The waves do not shift relative to one another The source of such waves is called coherent Sources that do not produce observable interference due to the waves not having a constant phase difference are called incoherent

Combining Light Waves Equation for Constructive Interference The path difference between two waves = an integer multiple of the wavelength d * sinθ = ±m * λ m = 0, 1, 2, 3… Equation for Destructive Interference The path difference between two waves = an odd number of half wavelengths d * sinθ = ±(m + ½) * λ m = 0, 1, 2, 3…

Demonstrating Interference You can produce interference patterns in light waves by passing the light through a single slit and then two parallel slits Monochromatic (single wavelength or color) light produces a pattern of alternating bright and dark bands Bright bands are formed from constructive interference Dark bands are formed from destructive interference White light or other polychromatic light produces bands of color The pattern will be indistinct because the different colors have constructive and destructive interference at different positions

Demonstrating Interference Path difference – the difference in the distance traveled by two beams when they are scattered un the same direction from different points Difference in the distance traveled by two interfering waves Distance between slits on a filter (for light waves) If the path difference is 0 or a whole number multiple of the wavelength, the waves are in phase and constructive interference results If the path difference is an odd multiple of ½ the wavelength, the waves are 180° out of phase and destructive interference results