2 nd & 3 th n.u.t.s. workshops gulu university naples federico ii university 5 – diffraction

$: 2 nd & 3 th N.U.T.S. Workshops Gulu University Naples FEDERICO II University 5 – Diffraction$
2nd & 3th N.U.T.S. Workshops

Gulu University

Naples FEDERICO II University

5 – Diffraction

5- Diffraction

2nd & 3th NUTS Workshop ( Jan 2010)

2

Huygens(–Fresnel) Principle 1

The Huygens principle is a method of analysis applied to problems of wave propagation.

It recognizes that each point of an advancing wave front is in fact the centre of a new secondary disturbance and the source of a new train of spherical waves.

The advancing wave as a whole may be regarded as the sum of all the secondary spherical waves arising from points in the medium already traversed.The Huygens view of wave propagation helps better understand a variety of wave phenomena, such as reflection, refraction, diffraction, interference, …

5- Diffraction


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Huygens Principle 2

1 2

At time t0 a plane wave front, propagating from left to right at a speed v, reach the position 1All the points of position 1 became sources of spherical waves expanding at speed v

After a time interval t, the radius of the spherical waves will be v t; the sum (envelope) of all the secondary spherical waves will give the new position of the plane wave front at 2

The same is in the case of spherical wave front

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Huygens Principle 3

-Any small area dΣ of wave front is source of secondary spherical waves with the same frequency f of the primary wave

-Amplitude of secondary wave is proportional to that of primary wave and area dΣ; varies as cos(

- The wave front is superposition of all spherical waves reaching P; wave front = envelope of all wave fronts of secondary waves

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Schematic representation of a plane wave

arriving on a single slit

Huygens Principle 4

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Interference

The term interference usually refers to the interaction of waves which are coherent with each other (because they come from the same splitted source) and have the same or nearly the same frequency.

The interaction depends on total phase difference = sum of path difference and initial phase difference (if the waves are from 2 or more different sources)

If the waves reaching a point P are in phase the

result is constructive interference, if out of

phase destructive interference occur.

W1

W2

W1+W2

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Destructive Interference

d 1d2

At the intersection of two directions the crest of blue wave and the through of red wave meet: it is destructive interference

There we have (d1-d2)=nλ/2 (n integer odd)

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Constructive Interference

d1

d 2

At the intersection of two directions the crests of blue wave and of red wave superpose: it is constructive interference

at maxima (d1-d2)=mλ (m integer)

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Diffraction

Light does not always travel in a straight line.It tends to bend around objects. This phenomenon is called diffraction.Any wave will diffract, including matter and acoustic waves.

Shadow of a hand illuminated by a Helium-Neon laser. Note the bright and dark lines around the fingers, they are caused by diffraction.

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Diffraction and Huygens principle

Diffraction Applet

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Slit Diffraction: the Idea

λ

r1

r2

a

if (r1-r2) = mλ constructive interference

(m integer)

if (r1-r2) = nλ/2 destructive interference

(n integer odd)Problem: we have to account for all the points (infinite) of the slit !!!

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Slit Diffraction: the Experiment

λ

r

a

x

x′

L

θ

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Slit Diffraction: the Solution

2

0 sin

sinsin

)(I

a

a

I

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Slit Diffraction: Maxima (& Minima)

a

mmaka

212sin

212

sin

2

sin

Maxim

a:

Minima: a

nnaka

sin

sin

2

sin

Slit Diffraction Applet

General behaviors:- The smaller the slit width, the 'wider' the resulting diffraction pattern;

- Diffraction angles are invariant under scaling: they depend only on the ratio wavelength/size of the slit;

- Different λ‘s peak at different angles.

m positive or negative integer; there is a mmax ?

n positive or negative integer; except n = 0 where there is the main maximum

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Slit Diffraction: Different λ

Different λ different location and width of maxima

with white light no diffraction pattern but … blurred image

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Nice Diffraction

Diffraction by spider netDiffraction by squared slit (using expanded red laser

pointer)

2 nd & 3 th n.u.t.s. workshops gulu university naples federico ii university 5 – diffraction

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