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DIFFRACTIONShrishail KambleShrishail Kamble

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.

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.

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 DiskIf 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.

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Fresnel Diffraction Fraunhoffer Diffraction

• The source and the screen are at

finite distance from the obstacle.

• The source and the screen or both are

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.

Distinguish between Fresnel & Fraunhoffer diffraction

Fresnel Diffraction Fraunhoffer Diffraction

• Incident wave fronts are cylindrical. • Incident wave fronts are planar.

• The phase of the secondary

wavelets is not the same at all the

points in the plane of the obstacle.

• The phase of the secondary

wavelets are the same at all the

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 PowerThe 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

Well 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.

Not 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.

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 are

perpendicular to 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 originating from the

corresponding points A and C.

• Path difference = AC Sinθ

= (AB + BC) Sinθ

= (a + b) Sinθ

• 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.

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.

XY = filed of view of the telescope i.e. screen,

The direction of the nth primary maximum for a wavelength λ is

given by,

The direction of the nth primary maximum for a wavelength λ+dλ is

given by,

..... (1)

..... (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