How Is the Third Dark Fringe Calculated in Diffraction Problems?

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In summary, the conversation discusses finding the distance on a screen from the center of the central bright fringe in the third dark fringe on either side. The problem involves light with a wavelength of 668 nm passing through a slit 6.73 x 10^-6 m wide and falling on a screen 1.85 m away. The solution is found using the equation sin (theta) = m (wavelength/width), where m is the number of the fringe and theta is the angle between the length and the area where the fringe resides. The book provides a solution of 0.576 m for the bright fringe, which may differ from the solution obtained using the given approach.
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cheechnchong
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Homework Statement



Light that has a wavelength of 668 nm passes through a slit 6.73 x 10^-6 m wide and falls on a screen that is 1.85 m away. What is the distance on the screen from the center of the central bright fringe in the third dark fringe on either side?

Homework Equations



I will discuss this in the attempt at the solution; however, my attempt will based on sin (theta) = m(wavelength/ width)

The Attempt at a Solution



I have drawn a diagram of what the problem basically states. Anyways...I first tried to find the angle between the length (1.85 m) and the area where the fringe resides (I called it X). So...my setup for the angle looks like this tan (theta) = x/1.85.

Then, knowing that sin(theta) is similar (~) to tan (theta) I proceeded to find the answer by setting up x/1.85 = 3 (668x10^-9 m/ 6.73 x 10^-6 m) and found that x = 0.55 m.

^I used this equation: sin (theta) = m(wavelength/ width). Just in case there is any confusion!

I am confused with the answer discrepensy from my book and my approach...the book has the solution 0.576 m for the bright fringe. I am not sure whether my approach is wrong OR that the discrepensy is fine...Please let me know - even if there is a mathematical error (which I don't think is the case).

I appreciate all the help I can Get!
 
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any help here?
 
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^^^^?
 

1. What is diffraction and how does it occur?

Diffraction is a phenomenon where waves, such as light or sound, bend around obstacles or through openings. This occurs when the wave encounters an obstacle that is similar in size to its wavelength.

2. What is the difference between single-slit and double-slit diffraction?

Single-slit diffraction occurs when a wave passes through a single slit, causing it to spread out and create a pattern of bright and dark fringes. Double-slit diffraction, on the other hand, occurs when a wave passes through two closely spaced slits, creating a more complex interference pattern.

3. What is the relationship between the size of the slit and the diffraction pattern?

The size of the slit is directly related to the width of the diffraction pattern. A smaller slit will produce a wider diffraction pattern, while a larger slit will produce a narrower pattern.

4. How does diffraction play a role in everyday life?

Diffraction is responsible for a variety of everyday phenomena, such as the rainbow colors seen in soap bubbles, the blurring of light around the edges of objects, and the interference patterns seen in CDs and DVDs.

5. How is diffraction used in scientific research and technology?

Diffraction is used in various scientific fields, such as X-ray crystallography to determine the structure of molecules, and in the development of diffraction gratings for use in spectrometers and other optical devices. It is also used in the study of earthquake waves to understand the structure of the Earth's interior.

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