Transcript 05 Diffraction - WordPress.com

DIFFRACTION
Shrishail Kamble
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 In his 1704 treatise on the theory of optical phenomena
(Opticks), Sir Isaac Newton wrote that "light is never known
to follow crooked passages nor to bend into the shadow".
 He explained this observation by describing how particles of
light always travel in straight lines, and how objects
positioned within the path of light particles would cast a
shadow because the particles could not spread out behind
the object.
 True, to a point.
 On a much smaller scale, when light waves pass near a
barrier, they tend to bend around that barrier and spread at
oblique angles.
 This phenomenon is known as diffraction of the light, and
occurs when a light wave passes very close to the edge of an
object or through a tiny opening, such as a slit or aperture.
Diffraction is a wave effect
Interference pattern of light and dark bands
around the edge of the object.
Diffraction is often explained in terms of the
Huygens principle, which states that each
point on a wavefront can be considered as a
source of a new wave.
All points on a wavefront serve as
point sources of spherical secondary
wavelets. After a time t, the new
position of the wavefront will be that
of a surface tangent to these
secondary wavefronts
Diffraction by a Single Slit or Disk
If light is a wave, it will diffract around a single slit or
obstacle.
What is diffraction?
Diffraction is the bending of light around the sharp edges of
an obstacle in order and produces bright illumination in
geometrical shadow region.
Diffraction becomes significant only when the obstacle
size is comparable with wavelength of incident light.
Distinguish between Fresnel & Fraunhoffer diffraction
Fresnel Diffraction
Fraunhoffer Diffraction
• The source and the screen are at
• The source and the screen or both are
finite distance from the obstacle.
effectively at infinite distance from the
obstacle.
• Observation of Fresnel diffraction
does not require any lenses.
•The
conditions
required
for
the
Fraunhoffer diffraction are achieved
using two convex lenses.
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Fresnel Diffraction
Fraunhoffer Diffraction
• Incident wave fronts are cylindrical. • Incident wave fronts are planar.
• The phase of the secondary
• The phase of the secondary
wavelets is not the same at all the
wavelets are the same at all the
points in the plane of the obstacle.
points in the plane of the obstacle.
• It is experimentally simple but the
mathematical analyses is complex.
• This diffraction is simple to handle
mathematically because the rays are
parallel.
Resolving Power
The ability of an optical instrument to produce separate
patterns of two close objects is known as resolving power.
Rayleigh’s Criterion of Resolution
According to Rayleigh criterion, two point sources are
resolvable by an optical instrument when the central maximum
in the diffraction pattern of one falls over the first minimum in
the diffraction pattern of the other and vice versa.
Just Resolved
Let us consider the resolution of two wavelengths λ1 & λ2 by a
grating. The difference in wavelengths is such that their
principal maxima are separately visible. There is distinct point
of zero intensity in between the two. Hence the two
wavelengths are well resolved.
Well Resolved
Again consider the case when difference in wavelengths is so
small that the central maxima corresponding to two wavelengths
come closer as shown in figure. The resultant intensity in this
case is quite smooth without any dip. This condition is known as
not resolved.
Not Resolved
Diffraction Grating
 Diffraction Grating is an optical device used to study the
different wavelengths contained in a beam of light.
 The device usually consists of thousands of narrow,
closely spaced parallel slits (or grooves).
 A transmission grating can be made by ruling parallel lines
on a glass plate with a fine diamond point.
 Number of lines ruled is generally ≈ 15,000 – 30,000 lines
per inch.
 The spaces between the lines are transparent to the light
and hence act as separate slits.
Grating Constant
a: width of transparent part
b: width of opaque region
Grating element = (a + b)
cm
cm
Theory of Transmission Grating
• Let XY is the grating
surface & MN is the
screen,
both
perpendicular
to
are
the
paper.
• AB is the slit and BC is
the opaque portion.
• The width of slit is a and the opaque spacing between any two
consecutive slit is b.
• Let a plane wavefront be incident on the grating surface.
• The point P will be central maximum.
• Consider the secondary
waves
travelling
in
a
direction inclined at an
angle θ with the direction
of the incident light.
• The intensity at point P1 will depend on the path difference
between
the
secondary
waves
corresponding points A and C.
• Path difference = AC Sinθ
= (AB + BC) Sinθ
= (a + b) Sinθ
originating
from
the
• If the incident light consists of more than one wavelength, the
beam gets dispersed and the angle of diffraction for different
wavelength will be different.
• Let, λ and λ + dλ: two nearby wavelengths present in incident
light.
• θ and θ + dθ: angles of diffraction corresponding to these two
wavelengths.
Resolving power of diffraction grating
The R.P. of grating is defined as the, ratio of wavelength λ
of any spectral line to the smallest difference in
wavelength dλ, between this line and a neighboring line
such that the two lines appear just resolved, according to
Rayleigh’s criterion.
Let a beam of light having two wavelengths λ and λ+dλ is
normally incident on the grating.
XY = filed of view of the telescope i.e. screen,
P1 = nth primary maxima
of
spectral
line
of
wavelength λ at any
angle of diffraction θn.
P2 = nth primary maxima
of
spectral
line
of
wavelength λ+dλ at any
angle of diffraction θn+
dθn.
The direction of the nth primary maximum for a wavelength λ is
given by,
..... (1)
The direction of the nth primary maximum for a wavelength λ+dλ
is given by,
..... (2)
These two lines appear just resolved if the angle of diffraction
(θn + dθn) also corresponds to the direction of the first
secondary minimum after the nth primary maximum at P1.
This is possible if the extra path difference is λ/N.
where, N – total number of lines on grating surface.
..... (3)
Equating R.H.S. of eqn (2) and (3)
Thus, the resolving power of a grating is independent of the
grating constant. The resolving power is directly proportional to,
(i) The order of spectrum and
(ii) The total number of lines on the grating surface.
The penetration of waves into the regions of geometrical shadow is -----------a) Interference b) polarization c) diffraction d) dispersion
In Fraunhoffer diffraction the wavefront undergoing diffraction has
to be ---------------a) Spherical b) cylindrical c) elliptical d) plane
Maximum number of orders possible with a grating is----------------a) Independent of grating element
b) Directly proportional to the grating element
c) inversely proportional to the grating element
d) Directly proportional to the wavelength
The criterion of resolution of optical instruments was given by -------a) Newton b) Huygen
c) Rayleigh d)Ramsden
The resolving power of grating having N slits in nth order will be-----a) (N+n)
b) (N-n )
c) nN
d) n/N
When white light is incident on diffraction grating, the light diffracted
more will be ----------a) Blue b) violet c) red d) yellow
In Fresnel diffraction, the distance of the source of light & the screen
or both from the obstacle is -------------a) Infinite b) finite c) 10m d) none of these
In Fraunhoffer diffraction, the distance of the source of light & the
screen from the obstacle is -------------a) Infinite b) finite
c) 10m d) none of these
The grating constant is given by the equation ---------------a)No. of lines per cm
c)2.54/ No. of lines per cm
b) No. of lines per inch
d) 1/No. of lines per cm
The resolving power of a grating is --------------a) λ/dλ
b)dλ/λ
c) nN/ dλ
d)n(n+1)
The resolving power of a grating is directly proportional to -------a)wavelength b)slit width c) distance of screen from grating
d) order of the spectrum
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