Diffraction of light when two fingers brought close together infront of a light source

Diffraction by razor blade when illuminated by intense blue light

“light is never known to follow

crooked passages nor to

bend into the shadow”.

Sir Isaac Newton (1642-1727)

“Any deviation of light rays from

rectilinear path which is neither

reflection nor refraction known

as diffraction.’’

Arnold Johannes Wilhelm Sommerfeld

(1868-1951)

Diffraction of Sound

Radio waves diffract around mountains.

When the wavelength is km long, a mountain peak diffract the wave.

Another effect that occurs is scattering – role of diffraction is not obvious.

Huygens’s Principle

“Every point in a propagating wavefront serves as the source

of spherical secondary wavelets, such that the wavefront at some

later time is the envelope of these wavelets.”

Huygens-Fresnel Principle

Every unobstructed point of a wavefront, at a given instant, serves as a

source of spherical secondary wavelets, The amplitude of the optical

field at any point beyond is the superposition of all these wavelets.

http://www.walter-fendt.de/ph11e/huygenspr.htm

Reflection and Refraction of waves© 2006 Walter Fendt

Christiaan Huygens(1629-1695)

Augustin Fresnel(1788-1827)

More refinement by Kirchhoff and Sommerfeld

Gustav Robert Kirchhoff(1824-1887)

Arnold Johannes Wilhelm Sommerfeld(1868-1951)

Classical model of diffraction

wavefrontobstacle

screen

On obstacle, the electron oscillator vibrating and reemittting at source frequency

Incident field and field of all vibrating electrons superpose in such away that there is zero field beyond the obstacle.

Assume the mutual interaction between the oscillators are essentiallynegligible.

Classical model of diffraction

Diffraction of a wave by a slit

Whether waves in water or electromagnetic radiation in air, passage through a slit yields a diffraction pattern that will appear more dramatic as the size of the slit approaches the wavelength of the wave.

Narrower the slit, the wider the pattern

A A AB B B

l>ABl<AB

Fraunhofer and Fresnel Diffraction

Joseph von Fraunhofer (1787-1826) Augustin Jean Fresnel

(1788 - 1827)

Fraunhofer vs. Fresnel diffraction

• In Fraunhofer diffraction, both incident and diffracted waves may be considered to be plane (i.e. both S and P are a large distance away)

• If either S or P are close enough that wavefront curvature is not negligible, then we have Fresnel diffraction

P

SS

P

•Fraunhofer limit diffraction

2ad

• If aperture (obstacle) has a width a

•Fresnel limit diffraction

2ad

d is the smaller of the two distances from S and S and P

•Fresnel diffraction pattern does change in shape as we move further away from the object (until, of course, we are so far away that the Fraunhofer condition is satisfied).

•The surface of calculation

http://www.rodenburg.org/theory/y1200.html

Fraunhofer or far field diffraction

Fresnel or near field diffraction

Fresnel –Fraunhofer Diffraction

Far from

the slit

zClose to the slit

Incident plane wave

1exp3exp

2expexpexp

niaia

iaiaaiAA

Superposition of N Oscillators

21exp

2sin

2sin

exp1exp1

nin

a

iinaA

2sin

2sin

n

A

21 n

2

0 2

sin ( / 2)*

sin / 2

nI AA I

2/cos4 2

I 1

0 0For

20

0

IIN

IN

IN

0 200 400 600

0.0

0.2

0.4

0.6

0.8

1.0

Inte

nsi

ty

Theta

2)]*10[sin( 2)][sin(

0 200 400 600

0

20

40

60

80

100

Inte

nsi

ty

Theta

2)]*10[sin(

2)][sin(

1. Optics Author: Eugene Hecht Class no. 535 HEC/O Central library IIT KGP