How Do You Calculate Unknown Wavelengths Using Diffraction Grating Formulas?

In summary, for a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 26°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 56°. Both angles correspond to the same order m of bright fringes. To solve for the unknown wavelength, the formula nλ = d sin θ can be used, but only for small angles. If the answer is not correct, the distances between the bright fringes will need to be taken into account.
  • #1
Laceb04
4
0
For a wavelength of 420 nm, a diffraction grating produces a bright fringe at an angle of 26°. For an unknown wavelength, the same grating produces a bright fringe at an angle of 56°. In both cases the bright fringes are of the same order m. What is the unknown wavelength?
________________nm


Info: The Diffraction Grating & Compact Discs, Digital Video Discs, and the Use of Interference


My answers all keep coming out wrong. I don't know what I'm doing!
 
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  • #2
Laceb04 said:
My answers all keep coming out wrong. I don't know what I'm doing!

It's hard for us to tell what you're doing wrong when you don't post your work. Let's see your attempted solution.
 
  • #3
According to the short cut formula
n lambda = d sin theta
just set up x sine angle to 420 sine angle ratio.
However, this only works for small angles.
If that does not give right answer, you have to distance ratios
 

1. What is a diffraction grating?

A diffraction grating is an optical component that consists of a large number of parallel, evenly spaced slits or grooves on a surface. When light passes through the grating, it is diffracted into multiple beams, creating a spectrum of colors.

2. How does a diffraction grating work?

A diffraction grating works by using the principle of diffraction, which is the bending of light as it passes through a narrow opening. The grooves on the grating act as narrow openings, causing the light to diffract and create a spectrum.

3. What is the difference between a reflection grating and a transmission grating?

A reflection grating reflects light off of its surface, while a transmission grating allows light to pass through it. Reflection gratings are typically made of metal, while transmission gratings are usually made of glass or plastic.

4. How is the spacing of the grooves on a diffraction grating determined?

The spacing of the grooves on a diffraction grating is determined by the wavelength of the light and the desired angle of diffraction. The spacing is typically very small, ranging from a few micrometers to nanometers.

5. What are some common applications of diffraction gratings?

Diffraction gratings have many applications in fields such as spectroscopy, telecommunications, and laser technology. They are also used in instruments such as spectrometers, monochromators, and optical filters.

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