Diffraction of spherical wave by plane grating

In summary, a plane monochromatic wave is diffracted by a plane grating, resulting in a diffraction pattern in the back focal plane when an ideal focusing lens is placed behind the grating. The geometric size of this pattern is proportional to the focal length of the lens. However, if the incident wave is divergent or convergent, the pattern will appear at a distance d larger or smaller than the focal length. It is believed that for a perfect lens, the diffraction pattern will still be planar and the distance will still scale. However, in reality, lens aberrations may complicate this concept.
  • #1
Philip Koeck
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Textbook examples usually involve a plane monochromatic wave that is diffracted by a plane grating.
If one places an ideal focusing lens behind the grating one will get a diffraction pattern in the back focal plane of the lens.
The geometric size of this diffraction pattern is proportional to the focal length of the lens.

Now if the incident wave is divergent or convergent then the diffraction pattern will end up at a distance d larger or smaller, respectively, than the focal length.

There are two things I'm wondering:

Is the diffraction pattern still sharp on a plane or on a curved surface?
Is the size of the diffraction pattern still proportional to the distance d?
 
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  • #2
I believe that for a hypothetical perfect lens the pattern will be planar and the distance will scale. Of course there are no perfect finite lenses in practice so we are now into the complicated world of lens abberations...I usually avoid this place.
 
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FAQ: Diffraction of spherical wave by plane grating

What is diffraction of spherical wave by plane grating?

Diffraction of spherical wave by plane grating is a phenomenon where a spherical wave of light passing through a plane grating (a series of parallel, equally spaced lines) is diffracted, or bent, in different directions. This results in a diffraction pattern of bright and dark spots, known as interference fringes.

How does a plane grating affect the diffraction of a spherical wave?

A plane grating affects the diffraction of a spherical wave by acting as a diffraction grating, which splits the incident wave into multiple waves that interfere with each other. The spacing of the grating lines determines the angle at which the diffracted waves will be observed.

What is the difference between diffraction of a spherical wave by a plane grating and a diffraction grating?

The main difference between the two is that a plane grating has parallel, equally spaced lines, while a diffraction grating has non-parallel, varying spacing between its lines. This results in different diffraction patterns, with the plane grating producing a simpler pattern of interference fringes.

What factors affect the diffraction pattern of a spherical wave by a plane grating?

The diffraction pattern of a spherical wave by a plane grating is affected by several factors, including the wavelength of the incident wave, the spacing of the grating lines, and the distance between the grating and the observation point. Additionally, the angle of incidence and the angle of observation also play a role in determining the diffraction pattern.

How is the diffraction pattern of a spherical wave by a plane grating used in practical applications?

The diffraction pattern of a spherical wave by a plane grating is commonly used in spectroscopy, where it is used to analyze the wavelengths of light emitted by a source. It is also used in diffraction gratings, which are used in optical instruments such as spectrometers and monochromators to separate and analyze light of different wavelengths.

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