Diffraction grating and red light

In summary, using a diffraction grating with 2469 lines/cm, the angle at which red light of wavelength 635 nm appears in first order can be calculated using the formula sin(theta) = m(lambda / d). The distance between each line in the grating is 1/2469 cm, resulting in an angle of 1.4735 e -6 degrees.
  • #1
Kris1120
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Homework Statement


White light is spread out into its spectral
components by a diffraction grating.
If the grating has 2469 lines/cm, at what
angle does red light of wavelength 635 nm
appear in first order?
Answer in units of ◦.


Homework Equations



sin(theta) = m([tex]\lambda[/tex] /d)

The Attempt at a Solution



theta = inverse sin [( 1 * 635 e-9 m) / 24.69 m} = 1.4735 e -6 degrees
 
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  • #2
Hi Kris1120,

Kris1120 said:

Homework Statement


White light is spread out into its spectral
components by a diffraction grating.
If the grating has 2469 lines/cm, at what
angle does red light of wavelength 635 nm
appear in first order?
Answer in units of ◦.


Homework Equations



sin(theta) = m([tex]\lambda[/tex] /d)

The Attempt at a Solution



theta = inverse sin [( 1 * 635 e-9 m) / 24.69 m} = 1.4735 e -6 degrees


In your formula, d is the distance between grating lines. If there are 2469 lines in every cm, what is the distance between each line?
 
  • #3
I see... its 1 / 2469 cm! Thank you!
 
  • #4
Kris1120 said:
I see... its 1 / 2469 cm! Thank you!

That's right (as long as you meant (1/2469) cm; some people inadverdently put the cm in the denominator for this type of problem).

Glad to help!
 

FAQ: Diffraction grating and red light

1. What is a diffraction grating?

A diffraction grating is an optical device consisting of a large number of parallel, equally spaced slits or grooves etched into a surface. It is used to separate and disperse light into its component wavelengths, similar to a prism.

2. How does a diffraction grating work?

A diffraction grating works by causing constructive and destructive interference of light waves as they pass through the slits or grooves. This results in the separation of the light into its component wavelengths, creating a spectrum.

3. What is the purpose of using a diffraction grating with red light?

The purpose of using a diffraction grating with red light is to separate and analyze the different wavelengths of red light, as well as any other colors present in the light source. This can provide valuable information about the composition and properties of the light source.

4. How is red light affected by a diffraction grating?

Red light is affected by a diffraction grating in the same way as any other color of light. It is dispersed into its component wavelengths, with longer wavelengths (such as red) being diffracted at a larger angle than shorter wavelengths (such as blue).

5. Can a diffraction grating be used to create a specific color of light?

Yes, a diffraction grating can be used to create a specific color of light by selectively filtering out certain wavelengths of light. By adjusting the spacing and number of slits on the grating, specific colors and wavelengths can be emphasized or blocked.

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