happyphysics.com Physics Lecture Resources Prof. Mineesh Gulati Head-Physics Wing Happy Model Hr. Sec. School, Udhampur, J&K Website: happyphysics.com

Ch 36 Diffraction © 2005 Pearson Education

Diffraction: Diffraction: Effects occurs when light strikes a barrier that has an aperture or an edge. The interference patterns formed in such a situation. Effects occurs when light strikes a barrier that has an aperture or an edge. The interference patterns formed in such a situation. Fresnel diffraction: diffraction which occur when both point source and the screen are relatively close to the obstacle. Fraunhofer diffraction: diffraction which occur when both point source and the screen are far enough to the obstacle diffraction which occur when both point source and the screen are far enough to the obstacle 36.1 Fresnel and Fraunhofer Diffraction © 2005 Pearson Education

36.2 Diffraction form a Single Slit © 2005 Pearson Education

dark fringes in single-slit diffraction © 2005 Pearson Education Horizontal slit

Example 36.1 You pass 633 nm laser light through a narrow slit and observe the diffraction pattern on a screen 6.0m away. You find that the distance on the screen between the centers of the first minima outside the central bright fringe is 32mm. How wide is the slit? You pass 633 nm laser light through a narrow slit and observe the diffraction pattern on a screen 6.0m away. You find that the distance on the screen between the centers of the first minima outside the central bright fringe is 32mm. How wide is the slit? ANS: ANS: © 2005 Pearson Education

36.3 Intensity in the Single-Slit Pattern © 2005 Pearson Education

intensity in single-slit diffraction © 2005 Pearson Education Amplitude in single-slit diffraction

© 2005 Pearson Education

Intensity Maxima in the single-slit pattern For a=λ For a=5λ

36.4 Multiple Slits © 2005 Pearson Education Constructive interference d sinθ= mλ

© 2005 Pearson Education Phasor diagrams for light passing through eight narrow slits

© 2005 Pearson Education Interference pattern for N slits

36.5 The Diffraction Grating intensity maxima, multiple slits © 2005 Pearson Education

Grating Spectrographs Chromatic resolving power

36.6 X-Ray Diffraction © 2005 Pearson Education Which used to verified that x-rays are waves and the atoms in a crystal are arranged in a regular pattern

© 2005 Pearson Education

Bragg condition for constructive interference from an array

© 2005 Pearson Education

36.7 Circular Apertures and Resolving Power diffraction by a circular aperture © 2005 Pearson Education

36.8 Holography © 2005 Pearson Education

Typical arrangement for hologram Laser Mirror 1 Beam expander Mirror 3 Mirror 2 Beam splitter Film © 2005 Pearson Education

Reconstruction Laser © 2005 Pearson Education

Diffraction occurs when light passes through an aperture or around an edge. When the source and the observer are so far away from the obstructing surface that the outgoing rays can be considered parallel, it is called Fraunhofer diffraction. When the source or the observer is relatively close to the obstructing surface, it is Fresnel diffraction.

Monochromatic light sent through a narrow slit of width a produces a diffraction pattern on a distant screen. Equation (36.2) gives the condition for destructive interference (a dark fringe) at a point P in the pattern at angle θ. Equation (36.7) gives the intensity in the pattern as a function of θ. (See Examples 36.1 through 36.3) © 2005 Pearson Education

A diffraction grating consists of a large number of thin parallel slits, spaced a distance d apart. The condition for maximum intensity in the interference pattern is the same as for the two- source pattern, but the maxima for the grating are very sharp and narrow. (See Example 36.4)

A crystal serves as a three-dimensional diffraction grating for x rays with wavelengths of the same order of magnitude as the spacing between atoms in the crystal. For a set of crystal planes spaced a distance d apart, constructive interference occurs when the angles of incidence and scattering (measured from the crystal planes) are equal and when the Bragg condition [Eq.(36.16)] is satisfied. (See Examples 36.5) © 2005 Pearson Education

The diffraction pattern from a circular aperture of diameter D consists of a central bright spot, called the Airy disk, and a series of concentric dark and bright rings. Equation (36.17) gives the angular radius θ 1 of the first dark ring, equal to the angular size of the Airy disk. Diffraction sets the ultimate limit on resolution (image sharpness) of optical instruments. According to Rayleigh’s criterion, two point objects are just barely resolved when their angular separation θis given by Eq. (36.17). (See Example 36.6)

END Visit: happyphysics.com For Physics Resources