Diffraction Grating Homework: Find the Distance of Bright Fringes

In summary, the conversation discusses the use of a diffraction grating with 400 slits/mm to create an interference pattern on a wall by shining red and green laser beams with different wavelengths. The question asks for the distance between the two m = 1 bright fringes when the two lasers are on top of each other. The attempted solution uses a small angle approximation, but this may not be accurate. Further analysis is needed to determine the correct solution.
  • #1
Barry Melby
31
0

Homework Statement


You shine a red (λ = 650 nm) laser beam and a green (λ = 532 nm) laser beam at a diffraction grating that has 400 slits/mm to create an interference pattern on a wall 2.30 m from the grating. If the two lasers are directly on top of each other, how far apart are the two m = 1 bright fringes from each other?

Homework Equations

The Attempt at a Solution



(650*10^-9)(2.30) / (1/400)(.001) - (532*10^-9)(2.30) / (1/400)(.001) = 0.10856 m

This is incorrect, however. What did I miss?
 
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  • #2
You calculation appears to assume a "small angle approximation". Check to see if the angles of diffraction for the two wavelengths are "small".
 

1. What is a diffraction grating?

A diffraction grating is a device that consists of a large number of equally spaced, parallel slits or grooves. It is used to separate light into its different wavelengths, creating a spectrum.

2. How does a diffraction grating work?

When light passes through a diffraction grating, it is diffracted by the slits or grooves, resulting in constructive and destructive interference. This causes the light to spread out into its component wavelengths, creating a diffraction pattern.

3. What is the distance between bright fringes in a diffraction grating?

The distance between bright fringes in a diffraction grating is determined by the spacing between the slits or grooves in the grating. This spacing is typically given in units of micrometers or nanometers.

4. How can I find the distance of bright fringes in a diffraction grating?

The distance of bright fringes in a diffraction grating can be found using the equation d sinθ = mλ, where d is the grating spacing, θ is the angle of diffraction, m is the order of the bright fringe, and λ is the wavelength of light.

5. What are some real-world applications of diffraction gratings?

Diffraction gratings are used in a variety of scientific and technological applications, such as spectroscopy, laser optics, and telecommunications. They are also commonly used in educational demonstrations to show the properties of light and the principles of diffraction.

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