Diffraction grating wavelengths question

In summary, the problem is asking for the two wavelengths of light that coincide at a certain angle of diffraction when passing through a diffraction grating with 2.50 x 105 lines per metre. The third order of one wavelength is equal to the fourth order of the other, and the wavelengths differ by 160 nm. Using this information, simultaneous equations can be set up to solve for the wavelengths, which are found to be 480 nm and 640 nm. The angle of diffraction at which this coincidence occurs is calculated to be 28.69 degrees. The person solving the problem is requesting confirmation of their procedure.
  • #1
ombudsmansect
29
0
Hey guys this is the problem i need to solve:

Light consisting of two wavelengths which differ by 160 nm passes through a diffraction grating with 2.50 x 105 lines per metre. In the diffracted light, the third order of one wavelength coincides with the fourth of the other. What are the two wavelengths and at what angle of diffraction does this coincidence occur?


Attempt:

Ok I am assuming the question is saying that 3 wavelengths of one type of light is the same length of 4 wavelengths of the other, and that these coinciding on a screen of some sort will give point of maximum constructive interference (bright spot). SO using this information and the fact that the wavelengths differ by 160nm I am trying to figure out a set of equations to solve this. its not a lack of equations but ill have to set up some simultaneous equations probabl to solve through this. So ifff naybodys interested and a solution jumps out at those who might like solving this sort of gear your help is appreciated as this Q is annoyin me :)
 
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  • #2
ok i assumed that wavelength of light of the third order was longer than that of the 4th order one so:

L_1 - L_2 = 160nm

and from nL= dsintheta


3L_1 = dsintheta

divided by

4L_2 = dsintheta

using all of this info i got L_2 = 480nm, L_1 = 640nm

now subbed back in any of these two wavelengths into nL = sintheta

and got theta = 28.69 degrees

if there anyone readin this that might be able to give me a thumbs up on my procedure it would be greatly appreciated
 

1. What is a diffraction grating?

A diffraction grating is an optical device that consists of a large number of equally spaced parallel slits or grooves. 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 diffracting light into its component wavelengths, or colors, based on the spacing of the slits or grooves on the grating. This spacing causes constructive and destructive interference of the light waves, resulting in a spectrum of colors.

3. What are diffraction grating wavelengths?

Diffraction grating wavelengths refer to the specific wavelengths of light that are separated and displayed in the spectrum produced by the grating. These wavelengths correspond to the colors of the visible light spectrum.

4. How are diffraction grating wavelengths measured?

Diffraction grating wavelengths can be measured using a spectroscope, which is a device that uses a diffraction grating to separate and measure the wavelengths of light. The grating is calibrated so that the spacing of the slits is known, allowing for accurate measurements of the wavelengths.

5. What factors affect the diffraction grating wavelengths?

The spacing of the slits or grooves on the grating is the main factor that affects the diffraction grating wavelengths. A smaller spacing will result in a larger separation of wavelengths and a broader spectrum, while a larger spacing will result in a smaller separation and a narrower spectrum. The angle at which the light passes through the grating can also affect the wavelengths observed. Additionally, the quality and material of the grating can also impact the diffraction pattern and resulting wavelengths.

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