From last time Waves Interference Thursday, Sep. 4 Please pick up pack of color sheets Phy208 Lecture 2 1 Interference of 2 speakers constructiv e interferenc e,loud tone destructive

interference quit tone crest troug h Thursday, Sep. 4 Phy208 Lecture 2 2 Question Suppose that the frequency of the sound wave increases by a factor of two. The adjacent maxima are A) Farther apart B) Closer together C) Same Higher frequency, -> shorter wavelength

Less path length diff required to make 1 wavelength diff. D) Need to know speaker spacing Thursday, Sep. 4 Phy208 Lecture 2 3 Math Analysis Constructive interference: =d sin = 0 =0 =d sin = 1 sin = / d = Path 2

340m / s v = = 0.34 fd (1000 / s)(1m) = 0.347 rad = 19.9 =d sin = 2 v sin = 2 /d = 2 fd Path 1 = Extra path length / d = sin = d sin d Thursday, Sep. 4

Phy208 Lecture 2 4 For small angles sin = /d for constructive interference Small angle approximation For small , sin with in radians e.g. sin = /d = 0.34 Exact value: 0.34 radians =0.347 radians

Approx breaks down for large Thursday, Sep. 4 Phy208 Lecture 2 5 Light waves Light is a wave just like sound. But can propagate in vacuum at speed c = 3x108 m/s Has same wave properties, e.g. c vac = f Can also propagate in glass, water, but slower Speed in medium = v = c/n c vac

med = = nf n Has same superposition / interference properties n = Index of refraction Thursday, Sep. 4 Phy208 Lecture 2 6 Interference of light Thursday, Sep. 4 Phy208 Lecture 2 7

Projection on screen Light wavelength much shorter than sound Interference fringes much closer together y /L = tan y Light beam Recordin g plate Foil with two narrow slits Thursday, Sep. 4 L Phy208 Lecture 2

8 Small-angle approximation =d sin = Extra path length y = position on screen = L tan Thursday, Sep. 4 sin tan y Extra path length = ~ d L for 0

Phy208 Lecture 2 9 Fringe separation & wavelength For bright fringes: extra path length = m y bright L = m m = 0, 1, 2 K d For dark fringes: extra path length = (m+1/2) L 1 y dark = m + m = 0, 1, 2 K d 2 Bright Fringe

separation = Thursday, Sep. 4 Phy208 Lecture 2 L d 10 Question A two-slit interference pattern is observed in air (n=1). Then the entire system is immersed in water (n=1.33). The interference fringes are A) 1.33 times closer together B) 1.33 times farther apart C) 2.66 times closer together D) 2.66 times farther apart E) Spacing unchanged Thursday, Sep. 4 Phy208 Lecture 2

11 Interference of multiple sources Evenly-spaced slits have maxima at same location as two-slits. Maxima become sharper, more intense Interference of multiple sources often called diffraction Thursday, Sep. 4 Phy208 Lecture 2 12 Diffraction gratings Diffraction grating is pattern of multiple slits. Very narrow, very closely spaced. Expect very narrow interference peaks. (15,000 lines/inch)x(1 inch/2.54 cm)x(100

cm/m)=5.9x105/m So a spacing of 1/(5.9x105/m) = 1.7x10-6 m = 1700 nm. 1700 nm Thursday, Sep. 4 Phy208 Lecture 2 13 Question Suppose white light is shined through a diffraction grating. What would the pattern on the screen look like? A) L y bright = m d m = 0, 1, 2 K

B) C) QuickTime and a TIFF (LZW) to decompressor are needed see this picture. QuickTime and a TIFF (LZW) to decompre are needed see this D) Thursday, Sep. 4

Phy208 Lecture 2 14 Phase difference Waves start in phase Travel different distances (extra path length = ) No longer in phase when combined (Phase diff ) =/2 = = =2 General reln: =2 Constructive: =2mm Thursday, Sep. 4 Phy208 Lecture 2 Destuctive: =2m(m+1/2) 15 Thin film interference

Black Colors changing with thickness Thursday, Sep. 4 Phy208 Lecture 2 16 Thin film interference no phase shift air: n=1 n>1 180 ( radians) phase shift /n

t If film is much thinner than wavelength, ~ no phase shift from extra path length But top reflection has 180 phase shift, bottom not Destructive interference for all wavelengths, film appears black Thursday, Sep. 4 Phy208 Lecture 2 17 Thicker parts 180 phase shift from reflection Phase difference comes from air: n=1

t n>1 vac/n Extra path length=2 t air: n=1 Phase difference = + 2 Reflection phase shift Thursday, Sep. 4 Phase shift from reflection (top) Phase shift from extra path length

Extra path length for normal incidence = 2t 2t = ( vac / n ) 2m constructive (2m 1) destructive # wavelengths in extra path length Phy208 Lecture 2

18 Constructive interference 1 2t = m + 2 n 2t = m n (m = 0,1,2K ) constructive interference (m = 0,1,2K ) Thursday, Sep. 4 destructive interference Phy208 Lecture 2 19

Biological iridescence Some organisms seem to reflect incredibly vivid colors. Not by pigmen, but interference! Thursday, Sep. 4 Phy208 Lecture 2 20 Morpho family butterfly scales Spacing ~ 170 nm Thursday, Sep. 4 Phy208 Lecture 2 21

2t1 2t 2 2 + 2 = 2m o /n o 2 o = ( nt1 + t 2 ) m o = 2(1.5 64nm + 217nm) = 446nm Thin-film interference,Phy208 multiple Thursday, Sep.like 4 Lecture 2 layers, multiple interfaces 22