Today 1/22  Light Interference: read Text 27.1,2  HW: 1/22 Handout “Interference (more than one frequency)” due Friday 1/24  Today: Questions? Example Problem Young’s Double Slit experiment  Peer Guidance Center Begins Wed afternoon Wit 209

A little review  Waves  Two types, transverse and longitudinal  Wave speed depends only on the medium  Period, Frequency, Amplitude--just like SHM  v = f  Interference  Superposition-- adding waves  It’s all about Path Length Difference,, and..  Sources “in” or “out” of “Phase”

Example: Two sources emit in phase What is the lowest frequency of sound that will produce destructive interference here? PL 1 = 2.0m PL 2 = 2.2m

Young’s Double Slit (like two speakers) Single frequency source Wave crests Wave troughs Dark and bright “fringes” on a screen In phase at the slits c c c c c d d d d

Young’s Double Slit (like two speakers) Single frequency source Wave crests Wave troughs Does the pattern expand or contract when: -the slits move closer together? -the wavelength increases? In phase at the slits

Always true for any interference problem Sources In Phase: Constructive if PLD = m Destructive if PLD = (m + 1 / 2 ) Sources Out of Phase: Constructive if PLD = (m + 1 / 2 ) Destructive if PLD = m PLD = “path length difference” m = 0, 1, 2, 3,… (I used “n” the other day)

Two slit geometry (screen far away) Screen PLD = d sin  (d = slit separation)  d   PLD d (close enough)

Two slit geometry Screen PDL = d sin  (d = slit separation)  d sin  = m constructive interference d sin  = (m+ 1 / 2 ) destructive interference When the sources (slits) are “in phase” d

A simpler picture Screen very far away (L) Two slits very close together (d)  d sin  = m constructive interference d sin  = (m+ 1 / 2 ) destructive interference When the sources (slits) and “in phase”

The m’s m = 0 m = 1 m = 2 m = 1 m = 2 m = 1 m = 0 m = 1 d sin  = m d sin  = (m+ 1 / 2 ) 0 “zeroth order” fringe 1 “first order” fringe 2 “second order” fringe

Distance between fringes, y m = 0 m = 1 m = 2 m = 1 m = 2 m = 1 m = 0 m = 1 L y  tan  = y/L

Example: m = 0 m = 1 m = 2 m = 1 m = 2 m = 1 m = 0 m = 1  Light with a wavelength of 500 nm passes through two closely spaced slits and forms an interference pattern on a screen 2m away. The distance between the central maximum and the first order bright fringe is 5 mm. What is the slit spacing? The light is in phase at the slits. tan  = 5mm / 2m  = 0.14° d sin  = m = 1(500 nm) d = 0.2 mm 5mm 2m

Example: Twin radio antennas broadcast in phase at a frequency of 93.7  MHz. Your antenna is located 150 m from one tower and 158 m from the other. How is the reception, good or bad? v wave  =  c  =  3  10 8 m/s PLD = 8 m Does this equal some m or some (m + 1 / 2 ) ? v = f = 3.2m Make two lists 0 3.2m 6.4m 9.6m 12.8m 1.6m 4.8m 8.0m 11.2m 14.4m m (m + 1 / 2 ) m The condition is met for destructive interference. Reception at that location is bad.