Diffraction
the ability of waves to bend around obstacles
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.
Newton tried to explain diffraction due to an attraction between
light particles and edge of the obstacle!!
Diffraction


Huygen’s principle
requires that the
waves spread out
after they pass
through slits
This spreading out of
light from its initial
line of travel is called
diffraction
• In general, diffraction
occurs when wave pass
through small openings,
around obstacles or by
sharp edges
Diffraction, 2

A single slit placed between a distant
light source and a screen produces a
diffraction pattern
• It will have a broad, intense central band
• The central band will be flanked by a series
of narrower, less intense secondary bands

Called secondary maxima
• The central band will also be flanked by a
series of dark bands

Called minima
Diffraction, 3

The results of the single slit cannot
be explained by geometric optics
• Geometric optics would say that light
rays traveling in straight lines should
cast a sharp image of the slit on the
screen
Single slit Diffraction

Diffraction occurs
when the rays leave
the diffracting object
in parallel directions
• Screen very far from
the slit
• Converging lens
(shown)

A bright fringe is seen
along the axis (θ = 0)
with alternating bright
and dark fringes on
each side
Single Slit Diffraction



According to Huygen’s principle,
each portion of the slit acts as a
source of waves
The light from one portion of the
slit can interfere with light from
another portion
The resultant intensity on the
screen depends on the direction θ
Single Slit Pattern
w
qc
l
sinqc = l/w
1. When the wavelength of the light (wave) gets smaller compared to
the slit size, the bright spot gets sharper (more particle-like).
2. When l ≈ w, qc  90 (more wave-like).
Diffraction Grating

The diffracting grating consists of
many equally spaced parallel slits
• A typical grating contains several
thousand lines per centimeter

The intensity of the pattern on the
screen is the result of the combined
effects of interference and diffraction
Diffraction Grating, cont

The condition for
maxima is
• d sin θbright = m λ



m = 0, 1, 2, …
The integer m is the
order number of the
diffraction pattern
If the incident
radiation contains
several wavelengths,
each wavelength
deviates through a
specific angle
Diffraction Grating, final

All the wavelengths are
focused at m = 0
• This is called the zeroth
order maximum


The first order
maximum corresponds
to m = 1
Note the sharpness of
the principle maxima
and the broad range of
the dark area
• This is in contrast to to
the broad, bright
fringes characteristic of
the two-slit interference
pattern
Diffraction Grating
provides much clearer and sharper interference pattern
and a practical device for resolving spectra.
Dr = dsinq = ml  Constructive
d
q
Q. A diffraction grating having 20,000 lines per inch is illuminated
By parallel light of wavelength 589 nm. What are the angles at
Which the first- and second-order bright fringes occur?
dsinq = ml
d = 0.0254/20000
= 1.27 x 10-6 (m)
First-order
sinq1 = ml/d
= 589 x 10-9/1.27 x 10-6
= 0.464
q1 = 27.6
Similarly,
sinq2 = 2 x 0.464
= 0.928
q2 = 68.1
Diffraction occurs when light passes a:
1.
2.
3.
4.
5.
Pinhole
Narrow slit
Wide slit
Sharp edge
All of the above
45
3 x 108 = f l
nano = 10-9
http://laxmi.nuc.ucla.edu:8248/M248_99/iphysics/spectrum.gif
X-ray Diffraction and Crystallography
3rd
2nd
1st
0th
1st
2nd
3rd
2nd-order bright fringe
2nd bright fringe
1 nanometer = 1 x 10-9 m
Interference in Thin Films

Interference effects are
commonly observed in thin films
• Examples are soap bubbles and oil
on water

Assume the light rays are
traveling in air nearly normal to
the two surfaces of the film
Interference in Thin Films, 2

Rules to remember
• An electromagnetic wave traveling from a
medium of index of refraction n1 toward a
medium of index of refraction n2 undergoes a
180° phase change on reflection when n2 > n1

There is no phase change in the reflected wave if n2
< n1
• The wavelength of light λn in a medium with
index of refraction n is λn = λ/n where λ is the
wavelength of light in vacuum
Interference in Thin Films, 3


Ray 1 undergoes a
phase change of
180° with respect
to the incident ray
Ray 2, which is
reflected from the
lower surface,
undergoes no
phase change with
respect to the
incident wave
Interference in thin films
Difference in two routes
Ds =
= 2x
+
(when qi << 1)
2x = ml
constructive
= (2m+1)l/2 destructive
Half –reflecting planes
x
For an arbitrary angle q
Ds = 2x/cosq
x
x
n
Difference in two routes Ds = 2x = mlf constructive
Wavelength in the film (not in air)
v = c/n = f lf
c = f l
lf = l/n