Interference (Physics 3)

if two waves with identical wavelengths interact, they combine to form

a resultant wave

the resultant wave has the same wavelength as the component wave

superposition principle

the displacement of the resultant wave at any instant equals the sum of the displacements of the component waves

resultant wave

the consequence of the interference between two waves

monochromatic

a light source that has a simple wavelength (single colored)

constructive interference

the component waves combine to form a resultant wave with the same wavelength but with an amplitude that’s greater than the amplitude of either of the individual component waves

the result of constructive interferences is

light that is brighter than the light from the contributing waves

destructive interference

the resultant amplitude is less than the amplitude of the larger component wave (the result is dimmer light or dark spots)

for two waves to produce a stable interference pattern,

the phases of the individual waves must remain unchanged relative to one another

if the crest of one wave overlaps the crest of another wave,

the two have a phase difference of 0 degrees (and are said to be in phase)

if the crest of one wave overlaps through the trough of the other wave,

the two waves have a phase difference of 180 degrees (and are said to be out of phase)

coherence

what waves have when the phase difference between two waves is constant and the waves don’t shift relative to each other as time passes (can be said to be coherent)

when two light bulbs are placed side by side,

no interference is observed

random changes occurring in the light from one bulb doesn’t necessarily occur in

the light from the other bulb

the phase difference between the light waves from two bulbs are

not constant

the light waves interfere but the conditions for the interference change with each phase change therefore,

no single interference pattern is observed (are said to be incoherent)

fringes

when monochromatic light is used, the light from two slits produce a series of bright and dark parallel bands

when light from two slits arrives at a point on the viewing screen where constructive interference occurs,

a bright fringe appears at that location

when the light from two slits combine destructively at a point on the viewing screen,

a dark fringe appears at that location

when a white-light source is used to observe interference,

the situation becomes more complicated

the interference pattern is stable or well defined at positions where

there is constructive interference between light waves of the same wavelength

when the waves arrive at the central point of the screen

they have travelled equal distances

when waves arrive in phase at the center of the screen,

constructive interference occurs and a bright fringe forms at that location

when two light waves combine at a specific point off the center of the screen,

the wave from the more distant slit must travel one wavelength farther than the wave from the nearer slit

if waves meet midway between the locations of the two bright fringes,

the first wave travels half a wavelength farther than the second wave (the first waver overlaps the crest of the second wave, giving rise to destructive interference)