Question

Which is valid when Fresnal distance is equal to D ( D =distance between the slit and screen]

Diffraction or ray optics

I know that diffraction is valid when it is much less than D ....

Greater than D then ray optics is valid

What if they are equal???

Pls ans in detail ☺

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Solution

I read about the geometrical limit of wave theory. The source from where I read had a slightly different explanation to provide than here(The more rigorous answer is too complicated for me to understand). Though I do not understand completely the easier method in the linked question either, I would like to understand what the source form where I read is trying to say:-

An Aperture of size aa illuminated by a parallel beam sends diffracted beam (the central maxima) in angular width approximately λ/aλ/a. Travelling a distance zz, it aquires the widthzλ/azλ/a due to diffraction. The distance at which this width equals the size of the aperture is called the fresnel distance. zF=a2/λzF=a2/λ. It is the distance beyond which the divergence of beam of width aa becomes significant. At distances smaller than zFzF, spreading due to diffraction is smaller than the width of the beam, and at distances greater than zFzF, spreading due to diffraction dominates over that due to ray optics(width aa of the aperture

An Aperture of size aa illuminated by a parallel beam sends diffracted beam (the central maxima) in angular width approximately λ/aλ/a. Travelling a distance zz, it aquires the widthzλ/azλ/a due to diffraction. The distance at which this width equals the size of the aperture is called the fresnel distance. zF=a2/λzF=a2/λ. It is the distance beyond which the divergence of beam of width aa becomes significant. At distances smaller than zFzF, spreading due to diffraction is smaller than the width of the beam, and at distances greater than zFzF, spreading due to diffraction dominates over that due to ray optics(width aa of the aperture

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