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# Diffraction part i

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Diffraction

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### Diffraction part i

1. 1. DiffractionDiffraction is a phenomenon in which light bends around an obstacle.Grimaldi in 1665 first observed it.Fresnel explained the phenomenon on the basis of wave theory oflight. The diffraction is due to the finiteness of the wavefront. The phenomenon of diffraction was explained by considering the mutualinterference of secondary wavelets originating from the various points ofthe wavefront, which are not blocked off by the obstacle. Types of diffraction: Fresnel diffraction Fraunhoffer diffraction
2. 2. DiffractionDifferences between Fresnel and Fraunhoffer diffraction ● Fraunhoffer diffraction Fresnel diffractionSource of light and the screen are Source of light and the screen areat very large distance from the at finite distance from the obstacleobstacleIncident wavefront is a plane Incident wavefront is a sphericalwavefront. wavefrontInitial phase of the secondary Initial phase of the secondarywavelets is same at all points in the wavelets is different at differentplane of the diffracting device. points in the plane of the diffracting device.Use of converging lens ortelescope is necessary for Visible by eyeobservationsDiffracted wavefront is plane. Diffracted wavefront is sphericale.g. grating e.g. zone plate
3. 3. Diffraction ● Fraunhoffer diffraction Intensity distribution in single slit diffraction: P A θ P 0 B
4. 4. DiffractionAs the wavefront is planar, the energy passing through unit area of the wavefront persecond is constant. The intensity associated with the wavefront is also constant overthe entire slit aperture.a: Width of the slit ABP: point of focus of incident waveP’: point at which secondary waves traveling at angle t are focused.dz : element of wavefront at co-ordinate (0,z)ρ : distance from P’ to dz.r: distance of screen from O
5. 5. DiffractionThe amplitude of the wavefront emitted by the element dz is proportional tolength and inversely proportional to ρ.At the point P’ it produces an infinitesimal displacement which is a sphericalwave expressed by adz dy = sin ( ωt−kρ ) ρ t ρ =kdz sin2π ( - T λ ) The resultant displacement at P’ due to the entire wavefront is +a/ 2 t ρ y = k ∫ sin2π −a/ 2 - dz T λ ( )
6. 6. Diffraction from the figure, ρ2 = x 2 + ( z 0 −z )2 0 and r 2 = x 2 +z 2 0 0 ∴ x 2 = r 2− z 0 2 0hence ρ 2 = r 2−z 2 + ( z 0 −z ) 2 0 2 2 2 2 =r −z 0 + z 0 +z −2z 0 z =r 2 +z 2 −2z0 z =r 2 1− [ 2 zz 0 r2 z2 + 2 r ]
7. 7. Diffractionfor Fraunhoffer diffraction,r >> z and z 2 r 2 is negligible as compared to 1. 2 ρ = r 1− 2 [ 2 zz 0 r2 ] now 2 4 ( zz 0 ) 2 [ 1− 2 zz 0 r 2 ] = 1− 2 zz 0 r 2 + r4 as ( zz 0 ) 2 4 <<1 r it can be neglected
8. 8. Diffraction Continued....