Diffraction

Diffraction

Diffraction

• When waves encounter obstacles, the bending of waves around the edges of an obstacle is called “DIFFRACTION”.

DIFFRACTION

SSA

B

FIG 1.1

Here we have a source s emitting waves having plane wavefronts.

As the wavefronts pass through the slit ab,they are diffracted and are able to reach even those regions behind ab which they would be unable to reach had the rays not bended.

One more thing to be noted here is that the shape of the wavefronts change as they pass through the slit.

The reason for this bending can be explained with the help of huygens principle.

Diffraction by single slit,& its pattern.

Huygen’s principle:-each particle lying on any wavefront acts as an independent secondary source and emits from itself secondary spherical waves.After a very small time interval, the surface tangential to all these spherical wavelets,gives the position and shape of the new wavefront.

It will be more clear from the following example of plane wavefronts.

Let p1,p2,p3,…pn be points very close to each other and equidistant from each other on the plane incident wavefront.

To obtain the new wavefront we consider p1,p2,..Pn as independent sources and circular arcs with same radius from each of these points.

Now the plane a’ tangential to all these imaginary surfaces gives the new wavefront.

We move on to using huygen’s principle for explanation of diffraction.

Consider figure 1.1

A A’P1

P2

P3

P4

PN

The dimensions of the slit are finite.As a result,applying huygen’s principle we can say that the new wavefront obtained will be something like the surface shown in figure.

Types of diffraction There are two types of diffraction. 1)Fresnal diffraction 2)fraunhoffer diffraction

Fresnel diffraction

S

Fraunhofer diffraction

S

I. FRESNAL DIFFRACTION

When the distance between the slit ab and source of light s as well as between slit ab and the screen is finite, the diffraction is called Fresnal diffraction.

In Fresnal diffraction the waves are either spherical or cylindrical.

I. FRAUNHOFER DIFFRACTION

If light incident on slit ab is coming from infinite distance, the distance between obstacle a and screen c is infinite, the diffraction is called Fraunhofer diffraction.

In Fraunhofer diffraction the incident waves should have plane wavefronts.

X-Ray Diffraction

• X-rays have wavelengths comparable to atomic sizes and spacings, about 10–10 m

• Crystals and molecules reflect X-rays in specific patterns depending on their structures

X-ray diffraction pattern of myoglobin

Interaction of X-Rays with Atoms

• Involves the electrons, primarily

Bragg Diffraction

Bragg’s Law

nd sin2

• W. H. Bragg and W. L. Bragg, 1913 (Nobel 1915)• Condition for constructive interference:

• Diffraction from different sets of planes in the crystal gives a picture of the overall structure

Single Slit Diffraction

We have seen how we can get an interference pattern when there are two slits. We will also get an interference pattern with a single slit provided it’s size is approximately (neither too small nor too large)

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Light

To understand single slit diffraction, we must consider each point along the slit (of width a) to be a point source of light. There will be a path difference between light leaving the top of the slit and the light leaving the middle. This path difference will yield an interference pattern.

Path difference of rays to P from top and bottom edge of slit

L = a sin destructive if L = m, m=1,2,…

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Light

P

(a/2) sin

sin = ma

(m 1, 2...) Destructive

Single Slit Diffraction

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Notice that central maximum is twice as

wide as secondary maxima

Sin = m / W, Destructive

Dark Fringes on screeny = L tanL (mW

Maxima occur for y= 0 and,

y L (m1/2)(W

m=1

m=1

L