Diffraction Grating number of slits

In summary, the conversation discusses finding the number of slits per centimeter of a diffraction grating designed to disperse the first-order visible spectrum through an angular range of 15.0 degrees. The equation d sin \theta = n \lambda is used, with d = 1/N. The participants discuss using a small angle approximation and making assumptions about the range of visible light in order to solve for d.
  • #1
Ginerva123
14
0
[SOLVED] Diffraction Grating

Homework Statement



Find the number of slits per centimeter of a grating designed to disperse the first-order visible spectrum through an angular range of 15.0. Find also the angles at which the first-order visible spectrum begins and ends.


Homework Equations



d sin [tex]\theta[/tex] = n [tex]\lambda[/tex]
d = 1/N


The Attempt at a Solution



Okay, if it's first order, then n = 1, I suppose, but lambda and theta are unknown and I need to get d to find N...
For the second part, once I have d, I can input 400 and 700 nm for lambda to get the two values for theta, but obviously I need d for both answers and I have no clue how to get it. Any help would be appreciated. Thanks!
 
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  • #2
I think for this you will just solve for d and you can use your good assumptions (400nm-700nm) for the range of visible spectrum. If you read the question carefully again it says 'designed to disperse the first-order visible spectrum through an angular range'. That means the angle from the start of the first order spectrum to the angle at the end of the first order spectrum has to be 15 degrees. Can you proceed from there?
 
  • #3
Bump. I had a look at this too.

If you have a RANGE of wavelengths, how can you solve for d with that equation?
 
  • #4
You might consider using the "small" angle approximation to simplify the algebra a bit.
The answer will be out by 10% or so.
 
  • #5
I'm sorry, but there just seems to be to many unknowns in the question for me... using a small angle approximation won't eliminate any of them, as far as I can see. Is there perhaps another equation I could use to find d?
 
  • #6
[tex] \Delta \theta = \theta_1 - \theta_2 [/tex] for a range of wavelengths. What is theta? You can rearrange the equation you gave above for theta.
 
  • #7
Theta = sin-1(n lambda / d)... but without values for lambda or d (my 400 - 700 nm are only approximations for the second part) how would I solve this? (My profuse apologies if I'm coming across as particularly obtuse here, but I just can't grasp this question!)
 
  • #8
You would use your assumptions. Like I said they are good assumptions for the range of visible light. Then you can solve for d.
 

FAQ: Diffraction Grating number of slits

What is a diffraction grating and how does it work?

A diffraction grating is an optical component that is used to separate light into its component wavelengths. It consists of a large number of parallel slits or grooves that are closely spaced together. When light passes through the grating, it is diffracted and the different wavelengths of light are separated based on their angles of diffraction.

How is the number of slits on a diffraction grating determined?

The number of slits on a diffraction grating is determined by the size and spacing of the slits, which are carefully calculated to produce the desired diffraction pattern. The spacing between the slits is typically measured in micrometers (μm) or nanometers (nm) and can range from a few hundred to several thousand per millimeter.

What is the relationship between the number of slits and the diffraction pattern?

The number of slits on a diffraction grating directly affects the diffraction pattern produced. As the number of slits increases, the diffraction pattern becomes sharper and more defined, with narrower peaks and valleys. This is because the more slits there are, the more light is diffracted and the greater the angle of separation between different wavelengths of light.

How does the number of slits on a diffraction grating affect the resolution of the spectrum?

The number of slits on a diffraction grating is directly related to the resolution of the spectrum. A higher number of slits results in a higher resolution, as there is a greater separation between the wavelengths of light. This allows for more accurate measurement and identification of different wavelengths in the spectrum.

What factors should be considered when choosing the number of slits on a diffraction grating?

When choosing the number of slits on a diffraction grating, factors such as the desired resolution, the wavelength range of the light, and the size of the grating should be taken into consideration. In general, a higher number of slits will result in a higher resolution, but may also decrease the overall intensity of the diffracted light. It is important to strike a balance between resolution and intensity when choosing the number of slits for a specific application.

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