Wave nature of light thin films diffraction Physics

Wave nature of light thin films, diffraction Physics 123, Spring 2006 11/3/2020 Lecture VI 1

Intensity in Young’s experiment • E=E 1 +E 2 • E=E 0 (sin(wt)+sin(wt+d)) • q=0 d=0: amplitude E(q=0)=2 E 0 • I(q=0)=4 E 02 • Amplitude E(q)=2 E 0 cos(d/2) • I(q)=4 E 02 cos 2(d/2) 11/3/2020 Lecture VI 2

Intensity in Young’s experiment • I(q=0)=4 E 02 • I(q)=4 E 02 cos 2(d/2) • Bright when cos=1, or -1 11/3/2020 Lecture VI 3

Young’s experiment • • • 11/3/2020 Lecture VI lr=700 nm lb=400 nm d=2000 nm L=20 cm First fringes (bright spots) yr, yb-? m=1: y=L l/d yr=7 cm yb=4 cm Blue is closer to the center than red 4

Young’s experiment • Two different - l 1, l 2 • Distance between slits – d • Multiple slits (diffractive grating) – same pattern, sharper lines 11/3/2020 • Interference pattern depends on l Lecture VI – Maxima: – d sinq 1 = m l 1 – d sinq 2 = m l 2 5

Coherence • Why do not we observe an interference pattern between two different light bulbs? • These two sources of light are incoherent: • What does it mean for two sources to be coherent? – Same (or close) frequency – Constant shift in phase (not necessarily zero) 11/3/2020 Lecture VI 6

Light in a medium (refraction) n 1 n 2 11/3/2020 Lecture VI • Huygens principle – each point forces oscillations with frequency f • f 1=f 2 • v 1=c/n 1 • v 2=c/n 2 • n 1 l 1=n 2 l 2 • E. g. go from air to medium n: • l l/n • ln=l/n 7

Light in medium d 1=k 1 x=(2 p/l 1)x=2 p 600/400=3 p + - l=400 nm x=600 nm Destructive interference n=2 + ln=l/n=400/2=200 nm Extra phase d=d 2 -d 1=3 p d 2=k 2 x=(2 p/l 2)x=2 p 600/200=6 p 11/3/2020 Lecture VI 8

Reflection of a transverse wave pulse • Reflection from fixed end –inverted pulse • Reflection from loose end – the pulse is not inverted. 11/3/2020 Lecture VI 9

Reflection + + - + • Reflect from medium with higher n 2>n 1 phase lower n 2<n 1 no phase change by d=p change d=0 – + 11/3/2020 – + + Lecture VI 10

Soap film • • • Soap film, air on both sides film is violet Thickness t 2 t=400 nm/2/n n(soap)=1. 42 t=70 nm n(soap)>n(air) Ray 1 d=p at A film is red n(air)<n(soap) Ray 2 d=0 at B 2 t=700 nm/2/n Relative shift d‘=p t=123 nm Ray 2 travels ABC = extra 2 t Violet is thinner d“=k. Dl=2 p 2 t/ln= 4 pt/ln than red. Relative shift d= d“-d’= 4 pt/ln-p If d=-p+2 pm 4 pt/ln=2 pm or t(m=1)=ln/2 – Rays 1 and 2 are out of phase – Destructive interference • If d=2 pm 4 pt/ln-p=2 pm or t(m=0)=ln/4 1 2 B – Rays 1 and 2 are in phase – Constructive interference 11/3/2020 Lecture VI 11

Diffraction on a single slit z Dl x 0 Slit size D, z=-D/2 to D/2 Observe diffraction at angle q Interference of waves coming from dz 11/3/2020 Lecture VI 12

Diffraction on a single slit Integrate over dz z Dl x 0 11/3/2020 Lecture VI 13

Diffraction • Dark spot at • Except q=0 – must be bright spot: 11/3/2020 Lecture VI 14

Diffraction • Single slit diffraction • Angular half width of the first peak: 11/3/2020 Lecture VI 15