Physics 203204 5 Interference Youngs DoubleSlit Experiment Intensity

Physics 203/204 5: Interference • Young’s Double-Slit Experiment • Intensity Distribution of the Double-Slit Interference Pattern • Phasor Addition of Waves • Interference in Thin Films

• In order to observe interference in light rays, light must be: • Coherent • Monochromatic • Superposition Principle must apply

In phase Out of phase x axis L r 1 d r 2 P; (x=0) y

path difference = r 2 - r 1 sin = d Þ = dsin = r 2 - r 1 approx. parallel 2 r as L >>d We get constructive interference when = dsin = ml, m = 0, ± 1, ± 2, K We get destructive interference when æ 1ö = dsin = ç m + ÷ l è 2ø

for small ml y » = = sin tan L d position of FRINGES l. L y bright = m d l. L y dark = m + 1 2 d Consider electric field intensity of the two interfering light waves at the point P ( ) E 1 = E 0 sin t E 2 = E 0 sin ( t + ) only depends on path difference l path difference of one wavelength c phase difference ofp 2 radians

l path difference of 2 c phase difference ofp radians l = Þ = l 2 p 2 p 2 p = = dsin l l i. e. = ( )

Electric field intensity at point P, Ep E p = E 1 + E 2 = E 0 (sin t + sin( t + )) = 2 E 0 cos sin ( t + ) 1 42 4 32 Amplitude = 0, 2 p, K Û constructive interference = p, 3 p, K Û destructive interference Intensity I of combined wave I µ E p 2

Intensity of an electromagnetic wave is given b 2 2 Emax. Bmax Emax c. Bmax I = Sav = = cuav 2 m 0 c 2 m 0 4 E 0 cos 2 2 2 = = 4 I 0 cos = Imax cos 2 m 0 c 2 2 2 Itot 2 æ pdsin ö = Imax cos ç ÷ è l ø 2 y as sin » we obtain L æ ö 2 pd Itot = Imax cos ç y÷ è l. L ø

can combine wavefunctions together using Phasor Diagram E 1(t) E 0 sin( t) = E 1(t) t Phasor representing electric field component E 1(t)

Etot E 2 E 1

Phasor diagram for 3 slit experiment E 3 Etot E 1 E 2

Interference by Thin Films white light 1 2 1800 phase change no phase change air soap air Get destructive and constructive interference depending on wavelength and position of observer: therefore see colors at different positions.

If ray 1 is 1800 out phase with ray 2 this ln is equivalent to a path difference of 2 é ù wavelength of light in medium ê ú lú ê whose refraction index is n andl n = ú êë nû ln if 2 t = rays will recombine in phase, in general 2 æ æ 1ö 1ö 2 t = ç m + ÷ l n Û 2 nt = ç m + ÷ l , m = 0, 1, 2, 3, K è è 2ø 2ø constructive interference 2 nt = ml, m = 0, 1, 2, 3, K destructive interference

Interference by Thin Films 1800 phase change white light 1800 phase change air oil water = m l , = 0, 1 , 2, 3, K constructive interference 2 nt æ m + è m 1 ö m l , ø 2 destructive interference = = 0, 1 , 2, 3, K t

Newtons Rings monochromatic light air acts as thin film