Diffractionthe ability of waves to bend around obstacles

Newton tried to explain diffraction due to an attraction betweenlight particles and edge of the obstacle!!

In 19th century, light is understood as a wave by work of Young and Fresnel and scientists searched for other wave phenomena

in light. One of them is diffraction.

DiffractionDiffraction Huygen’s principle Huygen’s principle

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

This spreading out of This spreading out of light from its initial light from its initial line of travel is called line 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 series The central band will be flanked by a series

of narrower, less intense secondary bandsof narrower, less intense secondary bands Called secondary maximaCalled secondary maxima

• The central band will also be flanked by a The central band will also be flanked by a series of dark bandsseries of dark bands

Called minimaCalled minima

Diffraction, 3Diffraction, 3

The results of the single slit cannot The results of the single slit cannot be explained by geometric opticsbe explained by geometric optics• Geometric optics would say that light Geometric optics would say that light

rays traveling in straight lines should rays traveling in straight lines should cast a sharp image of the slit on the cast a sharp image of the slit on the screenscreen

Single slit DiffractionSingle slit Diffraction DiffractionDiffraction occurs occurs

when the rays leave when the rays leave the diffracting object the diffracting object in parallel directionsin parallel directions• Screen very far from Screen very far from

the slitthe slit• Converging lens Converging lens

(shown)(shown) A bright fringe is seen A bright fringe is seen

along the axis (along the axis (θ = 0) θ = 0) with alternating bright with alternating bright and dark fringes on and dark fringes on each sideeach side

Single Slit DiffractionSingle Slit Diffraction According to Huygen’s principle, According to Huygen’s principle,

each portion of the slit acts as a each portion of the slit acts as a source of wavessource of waves

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

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

Single Slit Pattern

wc

sinc = /w

1. When the wavelength of the light (wave) gets smaller compared tothe slit size, the bright spot gets sharper (more particle-like).2. When ≈ w, c 90 (more wave-like).

Diffraction GratingDiffraction 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 combined screen is the result of the combined effects of interference and diffractioneffects of interference and diffraction

Diffraction Grating, contDiffraction Grating, cont The condition for The condition for

maximamaxima is is• d sin d sin θθbrightbright = m λ = m λ

m = 0, 1, 2, …m = 0, 1, 2, … The integer m is the The integer m is the

order numberorder number of the of the diffraction patterndiffraction pattern

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

Diffraction Grating, finalDiffraction Grating, final All the wavelengths are All the wavelengths are

focused at m = 0focused at m = 0• This is called the zeroth This is called the zeroth

order maximumorder maximum The first order maximum The first order maximum

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

the principle maxima the principle maxima and the broad range of and the broad range of the dark areathe dark area• This is in contrast to to This is in contrast to to

the broad, bright the broad, bright fringes characteristic of fringes characteristic of the two-slit interference the two-slit interference patternpattern

Diffraction Grating

d

r = dsin = m Constructive

provides much clearer and sharper interference patternand a practical device for resolving spectra.

Q. A diffraction grating having 20,000 lines per inch is illuminatedBy parallel light of wavelength 589 nm. What are the angles at Which the first- and second-order bright fringes occur?

dsin = m

d = 0.0254/20000 = 1.27 x 10-6 (m)

First-order sin = m/d = 589 x 10-9/1.27 x 10-6

= 0.464 1 = 27.6

Similarly, sin2 = 2 x 0.464 = 0.928 2 = 68.1

Diffraction occurs when light passes a:Diffraction occurs when light passes a:

45

1.1. PinholePinhole

2.2. Narrow slitNarrow slit

3.3. Wide slitWide slit

4.4. Sharp edgeSharp edge

5.5. All of the aboveAll of the above

http://laxmi.nuc.ucla.edu:8248/M248_99/iphysics/spectrum.gif

nano = 10-9

3 x 108 = f

X-ray Diffraction and Crystallography

0th

1st

1st

2nd

2nd

3rd

3rd

2nd-order bright fringe2nd bright fringe

1 nanometer = 1 x 10-9 m

Interference in Thin FilmsInterference in Thin Films

Interference effects are Interference effects are commonly observed in thin filmscommonly observed in thin films• Examples are soap bubbles and oil Examples are soap bubbles and oil

on wateron water Assume the light rays are Assume the light rays are

traveling in air nearly normal to traveling in air nearly normal to the two surfaces of the filmthe two surfaces of the film

Interference in Thin Films, 2Interference in Thin Films, 2

Rules to rememberRules to remember• An electromagnetic wave traveling from a An electromagnetic wave traveling from a

medium of index of refraction nmedium of index of refraction n11 toward a toward a medium of index of refraction nmedium of index of refraction n22 undergoes a undergoes a 180° phase change on reflection when n180° phase change on reflection when n22 > n > n11

There is no phase change in the reflected wave if nThere is no phase change in the reflected wave if n22 < n< n11

• The wavelength of light The wavelength of light λλnn in a medium with in a medium with index of refraction n is λindex of refraction n is λnn = λ/n where λ is the = λ/n where λ is the wavelength of light in vacuumwavelength of light in vacuum

Interference in Thin Films, 3Interference in Thin Films, 3

Ray 1 undergoes a Ray 1 undergoes a phase change of phase change of 180° with respect 180° with respect to the incident rayto the incident ray

Ray 2, which is Ray 2, which is reflected from the reflected from the lower surface, lower surface, undergoes no undergoes no phase change with phase change with respect to the respect to the incident waveincident wave

Interference in thin films

x

s =

Difference in two routes

+

2x = m constructive = (2m+1)/2 destructive

= 2x (when i << 1)

For an arbitrary angle

s = 2x/cos

Half –reflecting planes

x

x n

Difference in two routes s = 2x= m constructivef

Wavelength in the film (not in air)

v = c/n = f f

c = f f = /n