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Explain the importance of Fresnel distance. |
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Answer» Solution :An APERTURE of size .a. illuminated by a parallel beam sends diffracted light into an angle `theta` , then angular width `theta~~(LAMDA)/(a)` In travelling a distance z, the diffracted beam acquires a width `=ztheta` `=(zlamda)/(a)` due to diffraction The VALUE of z the spreading due to diffraction is EQUAL to the size of a of the aperture. `:.a=(zlamda)/(a)` `:.z=(a^(2))/(lamda)` This quantity is called the Fresnel distance `z_(F)`. `:z_(F)=(a^(2))/(lamda)` This equation shows that for distances much smaller than `z_(F)` the spreading due to diffraction is smaller compared to the size of the beam (That means moving in a straight LINE). Hence, spreading due to diffraction dominates over that due to ray optics and it shows that ray optics is valid in the limit of wavelength tending to zero. |
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