24.6 Diffraction24.6 Diffraction Huygen’s principle Huygen’s principle

requires that the requires that the waves spread out after waves spread out after they pass through slitsthey pass through slits

This spreading out of This spreading out of light from its initial line light from its initial line of travel is called of travel is called diffractiondiffraction In general, diffraction In general, diffraction

occurs when wave pass occurs when wave pass through small openings, through small openings, around obstacles or by around obstacles or by sharp edgessharp edges

Diffraction, 2Diffraction, 2

A single slit placed between a distant A single slit placed between a distant light source and a screen produces a light source and a screen produces a diffraction patterndiffraction pattern It will have a broad, intense central bandIt will have a broad, intense central band The central band will be flanked by a The central band will be flanked by a

series of narrower, less intense series of narrower, less intense secondary bandssecondary bands

Called secondary maximaCalled secondary maxima The central band will also be flanked by The central band will also be flanked by

a series of dark bandsa series of dark bands Called minimaCalled minima

Diffraction, 3Diffraction, 3 The results of the The results of the

single slitsingle slit cannot cannot be explained by be explained by geometrical opticsgeometrical optics Geometrical optics Geometrical optics

would say that would say that light rays traveling light rays traveling in straight lines in straight lines should cast a should cast a sharp image of the sharp image of the slit on the screenslit on the screen

Fresnel and Fraunhofer Fresnel and Fraunhofer DiffractionDiffraction

Relation of Fresnel diffraction to Fraunhofer Relation of Fresnel diffraction to Fraunhofer diffraction by a single slitdiffraction by a single slit

Fresnel Fraunhofer

Parallel rays

Fraunhofer DiffractionFraunhofer Diffraction

Fraunhofer Fraunhofer DiffractionDiffraction occurs occurs when the rays leave when the rays leave the diffracting object the diffracting object in parallel directionsin parallel directions

A bright fringe is A bright fringe is seen along the axis seen along the axis ((θθ = 0) with = 0) with alternating bright alternating bright and dark fringes on and dark fringes on each sideeach side

24.7 Single Slit 24.7 Single Slit DiffractionDiffraction

According to Huygen’s According to Huygen’s principle, each portion of principle, each portion of the slit acts as a source of the slit acts as a source of waveswaves

The light from one portion The light from one portion of the slit can interfere of the slit can interfere with light from another with light from another portionportion

The resultant intensity on The resultant intensity on the screen depends on the the screen depends on the direction direction θθ

Single Slit Diffraction, 2Single Slit Diffraction, 2 All the waves that originate at the slit are in All the waves that originate at the slit are in

phasephase Wave 1 travels farther than wave 3 by an Wave 1 travels farther than wave 3 by an

amount equal to the path difference (amount equal to the path difference (aa/2)sin/2)sinθθ If this path difference is exactly half of a If this path difference is exactly half of a

wavelength (180wavelength (180oo), the two waves cancel each ), the two waves cancel each other and destructive interference resultsother and destructive interference results

(a/2)sin(a/2)sinθ =θ = λ/2 (for first or n = 1) or a sin θ=λλ/2 (for first or n = 1) or a sin θ=λ In general, In general, destructive interferencedestructive interference occurs for occurs for

a single slit of width a single slit of width aa when when sinsinθθdarkdark==nλnλ / /aa nn = = 1, 1, 2, 2, 3, … 3, …

Single Slit Diffraction, 3Single Slit Diffraction, 3 The general features of The general features of

the intensity distribution the intensity distribution are shownare shown

A broad central bright A broad central bright fringe is flanked by much fringe is flanked by much weaker bright fringes weaker bright fringes alternating with dark alternating with dark fringesfringes

The points of constructive The points of constructive interference lie interference lie approximately halfway approximately halfway between the dark fringesbetween the dark fringes

QUICK QUIZ 24.1

In a single-slit diffraction experiment, as the width of the slit is made smaller, the width of the central maximum of the diffraction pattern becomes (a) smaller, (b) larger, or (c) remains the same.

24.8 Diffraction Grating24.8 Diffraction Grating

The diffracting grating consists of The diffracting grating consists of many equally spaced parallel slitsmany equally spaced parallel slits A typical grating contains several A typical grating contains several

thousand lines per centimeterthousand lines per centimeter The intensity of the pattern on the The intensity of the pattern on the

screen is the result of the screen is the result of the combined effects of interference combined effects of interference and diffractionand diffraction

Diffraction Grating, cont.Diffraction Grating, cont. The condition for The condition for maximamaxima is is

d d sinsinθθbrightbright==mλmλmm=0, 1, 2, …=0, 1, 2, …

The integer The integer mm is the is the order order numbernumber of the diffraction of the diffraction patternpattern

If the incident radiation If the incident radiation contains several wavelengths, contains several wavelengths, each wavelength deviates each wavelength deviates through a specific anglethrough a specific angle

Diffraction Grating, cont.Diffraction Grating, cont. All the wavelengths are All the wavelengths are

focused at focused at mm = 0 = 0 This is called the zeroth- order This is called the zeroth- order

maximummaximum The first order maximum The first order maximum

corresponds to corresponds to mm = 1 = 1 Note the sharpness of the Note the sharpness of the

principle maxima and the principle maxima and the broad range of the dark broad range of the dark areaarea This is in contrast to to the This is in contrast to to the

broad, bright fringes broad, bright fringes characteristic of the two-slit characteristic of the two-slit interference patterninterference pattern

Grating spectrometerGrating spectrometer

The light to be The light to be analyzed passes analyzed passes through a slit and is through a slit and is formed into a parallel formed into a parallel beam by a lens. The beam by a lens. The diffracted light leaves diffracted light leaves the grating at angles the grating at angles that satisfy that satisfy d d sinsinθθbrightbright==mλmλ

Diffraction Grating in CD Diffraction Grating in CD TrackingTracking A diffraction grating A diffraction grating

can be used in a three-can be used in a three-beam method to keep beam method to keep the beam on a CD on the beam on a CD on tracktrack

The central maximum The central maximum of the diffraction of the diffraction pattern is used to read pattern is used to read the information on the the information on the CDCD

The two first-order The two first-order maxima are used for maxima are used for steeringsteering