Diffraction Grating, Light with two wavelengths

In summary, the conversation discusses the use of a diffraction grating with 6000 lines/cm to separate light with wavelengths of 520 nm and 630 nm. It is suggested to use the relevant equation sinθ = mλ/d to calculate the angles for the first and second order maxima for each wavelength separately. This is because the angles of diffraction maxima are completely wavelength dependent. The principle of superposition is important in understanding the behavior of different wavelengths in diffraction.
  • #1
AlmonzoWilder
10
0

Homework Statement


Light with wavelengths of 520 nm and 630 nm passes through a diffraction grating containing 6000 lines/cm.

a. Sketch a diagram of the image produced from m=0 to m=2, labeling the order of each fringe.

b. Calculate the angles for the first and second order maxima that would appear on the screen.

Homework Equations


sin[tex]\vartheta[/tex] = m[tex]\lambda[/tex]/d


The Attempt at a Solution


If 6000lines/cm
Then,
d=1m/(6000linesx100cm/m)
d=1.6x10^-6 m/line
I'm not quite sure where to start, I don't need someone to solve it for me...just to help point me in the right direction, please?
Thanks in advance
 
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  • #2
You start from the "relevant equation" you have provided. You know the wavelength(s), you know d. To find the angle (from the sine), you need m. What is m for the first order maximum, what is m for the second order maximum?
 
  • #3
Okay, I follow to a certain extent...which wavelength do I use? Do I average them?
 
  • #5
No, I know what diffraction is. In my book the explanation and all the examples they give they only use one wavelength. I just don't know what to do with the two...calculate them induvidually?
 
  • #6
If you know what a diffraction grating does, then you should know what happens when you shine light that consists of two or more wavelengths. What does happen? Before you focus on a formula and what to put in it, it is a good idea to have a picture in your mind about what is going on here.
 
  • #7
The principle of superposition was used extensively to develop the theory behind diffraction. Try and use it to understand what's happening when you shine light through that consists of several wavelengths.
 
  • #8
Okay, I get what you are saying now, the difraction grating is used to separate the different wavelengths.
So I use the equation for each wavelength because the different wavelengths mean that they will have different angles for m=1, m=2 etc.
Am I on the right track or completely wrong?
 
  • #9
That's exactly correct. :) As can be seen in the equation, the angles of diffraction maxima are completely wavelength dependent.
Physically, this means that for a given path length, some wavelengths undergo constructive interference (When the path difference is an integer multiple of that particular wavelength) and some undergo destructive interference, and some interfere in a way that's in between.
 
  • #10
Okay, so wave interference will only appear when what?
Thanks so much for your help, I really appreciate it!
 

FAQ: Diffraction Grating, Light with two wavelengths

1. What is a diffraction grating?

A diffraction grating is an optical device that consists of a large number of parallel, closely spaced slits or lines. It is used to separate light into its component wavelengths by causing interference patterns.

2. How does a diffraction grating work?

When light passes through a diffraction grating, it is diffracted into multiple beams that interfere with each other, creating a pattern of bright and dark fringes. The spacing between the slits in the grating determines the angle at which the different wavelengths of light are diffracted, allowing for separation and analysis of the light.

3. What is the difference between a diffraction grating and a prism?

While both a diffraction grating and a prism can separate white light into its component wavelengths, they work in different ways. A prism uses refraction to bend light, while a diffraction grating uses diffraction to create interference patterns and separate the light.

4. Can a diffraction grating be used with light of more than two wavelengths?

Yes, a diffraction grating can be used with light of multiple wavelengths. However, the spacing between the slits must be carefully designed to allow for the separation of the desired wavelengths.

5. What are some practical applications of diffraction gratings?

Diffraction gratings have a wide range of applications in fields such as spectroscopy, astronomy, and telecommunications. They are used to analyze the composition of materials, measure the wavelengths of light, and create optical filters and devices.

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