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Array theorem and convolutions

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Presentation on theme: "Array theorem and convolutions"— Presentation transcript:

1 Array theorem and convolutions
Derive array theorem from convolution theorem

2 Review: Sketch the diffraction pattern of this rectangular slit
I got it mostly right I got it mostly wrong but I tried

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4 The E-field at the screen due to one slit is (centered at the origin)
Find and sketch the E-field at the screen due to due slits centered at y = ±h/2. I got it mostly right I got it mostly wrong but I tried

5 Diffraction of the light from a distant flashlight viewed through a black umbrella fabric.

6 2-slit Fraun. diffraction pattern

7 N-slits diffraction features
How many minor peaks are between the major peaks?

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9 N-slits, grooves,mirror-strips  diffraction grating
major peaks occur when: minor peaks occur when:

10 N-slits, grooves,mirror-strips  diffraction grating
Ratio of major to minor peak in I: a) N b) N2 b) N1/2 Width of major peak decreases as what power of N? a) 1/N b) 1/N2 b) 1/N1/2

11 Diffraction grating orders

12 Diffraction grating orders

13 Reflective gratings are “blazed”
Typical grating for visible to UV light: grooves/mm, 10 cm wide105 lines. Reflective gratings most common: lines cut in glass, replicated onto plastic blanks, coated with metal (aluminum)

14 Modern methods Blazed gratings put more light into a nonzero order

15 Resolving power of a grating
How much must l change so peak moves by half its width?

16 Spectrometer Put slits at f from mirrors. Grating in center

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