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BTF-09-041

PHY 121

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Diffraction.

Fresnels Assumption.

Rectilinear Propagation of Light.

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Discovered by Francesco MariaGrimaldi (1618-1663).

Coined the word diffraction.Latin word diffiringere meaning tobreak into pieces.

Normally a deviation from therectilinear propagation .

DISCOVERY

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1.DIFFRACTION

Apparent bending of waves around theedges of obstacles .

Characteristic property waves .

Occurs with all types of waves.

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Diffraction phenomena

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Diffraction pattern of disc

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Diffraction pattern of horizontal slit

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Diffraction pattern circular aperture

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The Diffraction Grating

Diffraction grating is an arrangement consisting of a large number ofparallel, closely spaced slits.

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Fraunhoffer & Fresnel Diffraction

Far

Near

Fraunhoffer pattern

Fresnel pattern

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SO

Q

R

M

N

C

X

Y

P

2.

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To obtain the resultant effect at a point P onthe screen, Fresnel assumed that ;

(1)A wavefront can be divided into a large number

of strips or zones called Fresnels zones.

(2)The resultant effect at any point on the screen

depends on combined effect of all the secondarywaves.

(3)Resultant effect at a point also depends on itsdistances from the particular zones.

(4)Obliquity with reference to the zone and thepoint.

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Due to the wave front at C, the effect will bemaximum at O and decreases with increasingobliquity.

It is maximum in a direction radially outwardsfrom C and it decreases in the oppositedirection.

Effect at a point due to the obliquity factor is

proportional to (1+cos ) where POC=.

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Considering the elementary wave front at C;

(1)At the point O,since =0; and cos =1;hence the resultant effect at O is maximum.

(2)At a direction tangential to primary wavefront at C i.e., along CQ,since =90; and cos =0;one half of the resultant at O.

(3)At a direction along CS , since =180; andcos =-1; resultant is zero.

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The property of secondary wave front

eliminates one of the main drawbacks in theHuygens principle.

As secondary wave front spread outs in alldirections from primary wave front as in case of

Huygens principle so back wave propagation isa tedious method of calculation.

But in Fresnels assumptions, there is no back

wave propagation and the rear wave amplitudeis zero.

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3.Rectilinear Propagation of Light

P

B

A

D

C

X

Y

b

m3

m2

m1

o

m1

m2

m3

x

y

b

b+/2

b+3/2b+2/2

P

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O

m1

m2

m3

m4

4 3 2 1

Fresnels halfperiod zones

(or) half periodelements

Phase difference (or)

Path difference /2

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OP=b; OM1=r1; OM2=r2; OM3=r3; etc,..

M1P=b+/2; M2P=b+2/2; M3P=b+3/2; etc,

Area of 1st half period zone is (OM1)=[M1P - OP]

=[(b+/2)- b]

=[b+/4]

=b (app.,)..(1)

( is small, is negligible)

Radius of 1

st

half period zone r1=OM1=b..(2)Radius of 2ndhalf period zone OM2=r2=2b(app.,)(3)

Area of 2nd half period zone =[OM2-OM1]

=[2b-b]=b(4)

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m1

m2

m3

m4

m5

m6

m7

m8

m2=(m1+m3)/2

Resultant amplitude (A)=

m1-m2+m3-m4+..+mn

(if n is odd)

A=m1-m2+m3-m4+..-mn(if n is even)

A=m1/2+[m1/2-m2+m3/2]+[m3/2-m4+m5/2]+.

A=m1/2+mn/2. If n is odd

A=m1/2+mn-1/2-mn if n is even

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Number of half zones are infinite then,

n; then amplitudes of mn, mn-1 tendsto be zero;

A=m1/2+mn-1/2-mn

A=m1/2+0+0+..

then A=m1/2 ;

Im1/4; (I A )Where, I is intensity at point P due to thewhole wave front ABCD.

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If the size of the obstacles iscomparable to the wavelength of light , itis possible to observe the illumination inthe region of geometrical shadow also.

Thus, Rectilinear Propagation of light isonly approximately true.

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PRESENTED BY : A.Vigneshwaran

ROLL NO. : BTF-09-041