What are g and a in a Diffraction Grating Problem?

In summary, the conversation discusses a diffraction grating with a period of D and elements consisting of pairs of narrow slits separated by D/N, where N is an integer. The diffraction pattern when the grating is normally illuminated is sketched. The relative intensities of the various diffraction peaks of order n are calculated for the case N=4 and it is determined which peaks are forbidden. It is also shown that for the case N=2, the solution reduces to that of a simple grating with a period of D/2. The conversation also mentions the incorrect attempt at solving the problem and the need for a complete function for the grating to manipulate. Lastly, the concept of a double-slit effect is brought up
  • #1
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Homework Statement


A diffraction grating has period D, and each element of the grating consists of a pair of narrow slits separated by D/N where N is an integer.
a) Sketch the diffraction pattern when the grating is normally illuminated
b)Calculate the relative intensities $I_n$ of the various diffraction peaks of order n, for the case N=4. Which peaks are forbidden?
c)For the case N=2 show that the solution reduced to that of a simple grating of period D/2.

Homework Equations



See step 3 for my full attempt to solve the problem.

The Attempt at a Solution



I am aware that the above solution is incorrect, because I ended up ignoring so many things that the solution equals to the one for a double slit, but superposed on a comb of delta functions. My problem is that I don't know how to write the complete function of the grating as a simple function which one could nicely manipulate. Could someone please point me in the correct direction?

P.s I am aware that my attempt of the solution is not the most clear.

P.s.s Link to the higher resolution picture here.
 

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  • #2
"narrow slits" -> you can ignore single-slit effects. There is no envelope.

The pattern there is for the grating. You can see which phase you get between the two slits for those peaks.
What are g and a?
 

FAQ: What are g and a in a Diffraction Grating Problem?

What is a diffraction grating problem?

A diffraction grating problem is a scientific problem that involves analyzing the diffraction patterns produced by a grating, which is a surface with a series of parallel lines or slits. This is commonly used in optics and spectroscopy to disperse light into its component wavelengths.

How does a diffraction grating work?

A diffraction grating works by causing light to diffract, or bend, as it passes through a series of evenly spaced slits on a surface. This causes the light to spread out into its component wavelengths, creating a distinct pattern of bright and dark spots called a diffraction pattern.

What factors affect the diffraction pattern produced by a grating?

The main factors that affect the diffraction pattern produced by a grating are the spacing between the slits on the grating, the wavelength of the incident light, and the angle at which the light is observed. Additionally, the number of slits on the grating and the width of the slits can also have an impact on the diffraction pattern.

How is a diffraction grating problem solved?

To solve a diffraction grating problem, the pattern produced by the grating must be analyzed using mathematical equations such as the grating equation and the Rayleigh criterion. These equations take into account the factors that affect the diffraction pattern and can be used to determine the properties of the incident light, such as its wavelength.

What are some real-world applications of diffraction grating problems?

Diffraction grating problems have various real-world applications, including in the study of atomic and molecular spectra, identifying the composition of materials in chemistry and materials science, and in the development of optical instruments such as spectrometers and telescopes. They are also used in various industries, such as in the production of holographic images and in laser technology.

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