Diffraction

diff1.jpg (957 bytes)


Previously Asked Questions

Q:     What are Fresnel lenses and why are they so powerful?

A:   

Q:    Why does a compact disc show a rainbow of colors?

A:    The grooves in a compact disc are very fine/small/tiny and close to each other to distances comparable to typical wavelengths in the visible range.  Different light rays reflected on different grooves subsequently interfere and reinforce or cancel different wavelengths (and consequently different colors) depending on the angle of incidence.  Everybody knows that when one looks at a CD from different angles, one sees different rainbow of colors.

Q:     Certain sunglasses use polarizing materials to reduce the intensity of light from shiny object.  What orientation of polarization should the material have to be most effective?

A:    The orientation of polarization is irrelevant, since the human eye is insensitive to it.   The role of polarizing sunglasses is to reduce the net intensity of light entering the eye.  Any polarizer will allow only half of the intensity of a light source to pass through it.

There is though a particular case, when polarizing sunglasses are supposed to reduce the intensity of a light beam reflected by the surface of a lake.  When the light coming from the sun falls on the surface of the lake at an incidence angle equal to the Brewster angle, the reflected portion of it is totally polarized with a direction of polarization parallel to the surface of the lake.  If this reflected light is too bright to be view directly by the human eye, polarizing sunglasses can be used that decrease the brightness of this light ray.  In this case, the direction of polarization of the polarizer glasses should be different from horizontal.

Remember the Brewster phenomenon: At a certain angle of incidence of a light ray on the surface of water, part of the incident ray is reflected and part of it is refracted, and the reflected and refracted rays are at an angle of 90 degrees with each other.  In this case, the reflected ray is fully polarized in a direction parallel to the surface of the water.

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References

Definitions

Diffraction: a modification which light undergoes in passing by the edges of opaque bodies or through narrow slits or in being reflected from ruled surfaces and in which the rays appear to be deflected and to produce fringes of parallel light and dark or colored bands; also : a similar modification of other waves (as sound waves)

Equations

Single-slit diffraction minima Minima located at angles theta2.gif (833 bytes) to the central axis that satisfy
a sin theta2.gif (833 bytes) = mlambda2.gif (834 bytes)      for m = 1, 2, 3, . . .
Intensity of a single-slit diffraction pattern at any given angle theta2.gif (833 bytes) 37-5.gif (515 bytes)
Im is the intensity at the center of the pattern.
Circular aperture diffraction first minimum First minimum located at an angle theta2.gif (833 bytes) given by
37-12.gif (216 bytes)
Rayleigh's criterion for object on the verge of resolvability 37-14.gif (190 bytes)
Double-slit diffraction intensity 37-19.gif (393 bytes)
Multiple-slit diffraction maxima d sin theta2.gif (833 bytes) = mlambda2.gif (834 bytes)      for m = 0, 1, 2, . . .
Multiple-slit diffraction half-widths of maxima 37-28.gif (251 bytes)
Diffraction grating dispersion D 37-29.gif (283 bytes)
Diffraction grating resolving power R 37-32.gif (227 bytes)
X-ray diffraction - Bragg's law 2d sin theta2.gif (833 bytes) = mlambda2.gif (834 bytes)      for m = 1, 2, 3, . . .

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List of Topics

Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses
Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference
Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction
Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization  

 

 

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