Central fringe of blue light

In summary, the conversation is about a problem involving a narrow beam of light directed at a single slit and a blue filter placed in its path. The question is to calculate the width of the central fringe on a white screen based on the given information. The correct equation to use is W= (2 x wavelength x D)/a, but the variables D (distance from slit to screen) and a (width of the slit) are not necessary for this problem. The solution is fairly simple once you understand the characteristics of the diffraction pattern and realize that the central fringe is special. The correct answer is not 3.32nm, as the central fringe is being asked for, not the width of the slit.
  • #1
aurao2003
126
0

Homework Statement


Hi

It is I again! Can someone please tell me where I went wrong? My answer is all over the place!



A narrow beam of light is directed normally at a single slit. The diffracted light forms a pattern on a white screen. A blue filter is placed in the path of the beam before it reaches the slit. The distance across five fringes including the central fringe is 18mm. Calculate the width of the central fringe




Homework Equations



Using W= (2 x wavelength x D)/a





The Attempt at a Solution


Solution:

Wavelength = 475nm (450-495 range)

D = 18mm

a= 5 (?)





I got 3.32nm!



Anybody?
 
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  • #2
aurao2003 said:
A narrow beam of light is directed normally at a single slit. The diffracted light forms a pattern on a white screen. A blue filter is placed in the path of the beam before it reaches the slit. The distance across five fringes including the central fringe is 18mm. Calculate the width of the central fringe
[...]
Using W= (2 x wavelength x D)/a
That's the equation for the width of the central fringe, yes. But I don't think it's all that necessary for this problem.
Wavelength = 475nm (450-495 range)
That's a nice shade of blue. :smile:
D = 18mm
I think that D is the distance from the slit to the screen. That distance isn't given in the problem statement, but it turns out that you don't really need it for this problem.

[Edit: the 18 mm value is the distance spanning the central fringe plus 4 other fringes. You do need that for this problem. My original point is that the variable D is the distance from the slit to the screen, which is not necessary to know for this problem.]
a= 5 (?)
I think that a is the width of the slit. It's not given in the problem statement either, but it turns out that it's not necessary to solve this problem.
I got 3.32nm!
Something is not right! :eek:

Keep in mind the problem statement is asking for the width of the central fringe, not the width of the slit!

The problem gives you with width of the central fringe plus four other fringes.

Your job is to calculate the width of the central fringe, without the four other fringes.

The solution is pretty easy if you know basic characteristics of what the diffraction pattern looks like. (Hint: the trick is to realize that the central fringe is special compared to the other fringes. :wink:)
 
Last edited:

1. What is the central fringe of blue light?

The central fringe of blue light, also known as the zero order fringe, is the brightest and most central fringe in a diffraction pattern. It is characterized by the presence of a bright spot in the center, surrounded by progressively dimmer fringes.

2. How is the central fringe of blue light formed?

The central fringe of blue light is formed through the process of diffraction, where light waves bend and spread out as they pass through a small opening or around an obstacle. This causes the light waves to interfere with each other, resulting in a pattern of bright and dark fringes.

3. What is the significance of the central fringe of blue light?

The central fringe of blue light is significant because it provides information about the size and shape of the diffracting object. By analyzing the spacing and intensity of the fringes, scientists can determine the size of the opening or the dimensions of the obstacle.

4. How does the size of the diffracting object affect the central fringe of blue light?

The size of the diffracting object affects the central fringe of blue light in that a smaller object will produce a wider and brighter central fringe, while a larger object will produce a narrower and dimmer central fringe. This is due to the fact that smaller objects cause more diffraction, resulting in a larger number of fringes.

5. Can the central fringe of blue light be observed in everyday life?

Yes, the central fringe of blue light can be observed in everyday life. It can be seen when light passes through a small opening, such as a pinhole, or when light waves interact with small particles, such as dust or water droplets. It can also be observed in natural phenomena, such as the diffraction of sunlight through clouds or the interference of light waves on the surface of a soap bubble.

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