LECTURE 20: Interference, Diffraction, Resolution. Interference. Interference: Double Slit (for very narrow slits) Interference: Double Slit (DEMO)

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1 LECTURE 0: Interference, Diffraction, Resolution Interference *Three ways in which the phase ifference between two waves can change: 1. By traveling though meia of ifferent inexes of refraction. By traveling along paths of ifferent lengths 3. By reflection from a bounary A wave will unergo a 0.5 wavelength phase shift if it reflects off a meium with higher inex of refraction 11/7/10 Interference: Double Slit (for very narrow slits) Interference: Double Slit (DEMO) *The phase ifference between two waves can change if the waves travel paths of ifferent lengths. Flaring of light Interference maxima for m = m, m = 0,1,,... Interference minima for m = m + 1, m = 0,1,,... He, Ne laser (Coherent light source) two slits Laser (Light Amplification by Stimulate Emission of Raiation) Interference patterns visible on screen 11/7/ /7/10 4 1

2 Diffraction Diffraction from a Disk * When a wave encounters an ege, obstacle, or aperture with a size comparable to its wavelength ( ), those waves sprea out. This effect is calle iffraction. This regime is calle wave optics (geometrical optics is no longer a goo approximation). * Let us consier the case of light impinging on a small isk. We observe: 1) bright spot in the center. ) iffraction rings outsie an insie the geometrical shaow area Geometrical Optics (black lines) * The bright spot at the center was preicte by Fresnel in 1818 an observe by Arago. In wave optics (re lines) the two waves that touch the top an bottom of the isk travel the same istance to the center an therefore interfere constructively 11/7/ /7/10 6 Fresnel Diffraction (view of the intensity at screen) Diffraction (DEMO using razor blae) plane wave intensity plane wave cylinrical obstacle center bright spot: consistent only with wave theory. Counter-intuitive result! obstacle iffraction pattern 11/7/ /7/10 8

3 Diffraction from a Single Slit (screen far away) Consier a monochromatic wave incient on a place with a narrow slit. Diffraction from a Single Slit 11/7/ /7/10 10 Diffraction from a Single Slit Diffraction from a Single Slit a Represent the slit as a number of point sources of equal amplitue. Divie the slit into two an pair a point from the upper half with its partner in the lower half. When asin θ =, estructive interference between the paire rays occurs. (first minimum) Locations of minima for single - slit iffraction : a m = m, m = 1,,3,... a sin θ = (location 1st min) 1 a = (location n min) tan θm = y m L 11/7/ /7/10 1 3

4 Diffraction from a Single Slit smaller aperture, iffraction broaening θ = a Diffraction from a Single Slit (DEMO) laser Intensity larger aperture, less flaring of light plane wave with wavelength Seconary maxima are weak. slit with a 11/7/ /7/10 14 Diffraction from a Circular Aperture (DEMO) The iffraction pattern of a circular aperture (opening) of iameter is similar to a single slit of with a. a 1 st min n min 3 r min 1 = 1. =.3 3 = /7/10 15 Diffraction from a Circular Aperture The bright fringes are at: 1 = 1.63 =.68 3 = 3.70 Image of two nearby binary stars but iffraction patterns overlap The Airy isk limits the resolvability of nearby objects 11/7/

5 Rayleigh Criteria The minimum angular separation α c of two marginally resolvable points is such that the maximum of the iffraction pattern from one falls on the first minimum of the iffraction pattern of the other, The first minima is at α sin θ = 1. Therefore C = θ = sin Central max on first min. Not resolve Resolve Barely resolve 11/7/10 17 Rayleigh Criteria If α> α C objects can be resolve If α< α R objects can not be resolve To increase our ability to istinguish objects we must minimize the iffraction pattern. Because we can : increase or ecrease αc 1. 1) Use ultraviolet light (shorter ) Also epens on relative brightness an air turbulence in atmosphere ) e- beam use in Scanning Electron Microscopes (SEM) have (light)/10 5 3) place object uner a microscope in a rop of oil n =/n (to change the wavelength) 11/7/10 18 Rayleigh Criteria When αc 1. Diffraction Gratings (use to etermine of light) What happen if we go from slits to N slits? The fringes become narrower an faint seconary maxima appear between the fringes ( Δθ hw = half-with of central line). N If N is large (N/ 10 4 /cm) the fringes are very sharp an the seconary maxima can be neglecte an you have a grating. 1 θ δ θ = grating spacing N( lines) 5000lines rulings = cm cm cm 1 4 = = cm = 10 cm N 5000 δ = pathlength ifference = 11/7/ /7/10 0 5

6 Diffraction Gratings (DEMO) Sharp bright fringes occur if δ = sin θ = m m = 0,1, where m is the orer of the maxima. Grating are use to measure = m By etecting maxima of the iffraction pattern with m=1,, Resolving power R = = mn Δ 11/7/10 1 Diffraction Gratings (DEMO) For a given wavelength an, if N increases the half-with ecreases Δ θ = hw N 11/7/10 6