Calculating Minimum Angle in Multiple-Slit Interference

In summary, the conversation was about using the correct formula for determining the angle (measured relative to the normal to the screen) to the minimum closest to the center of the screen in a five-slit mask with a distance of 125*[lambda] between adjacent slits. The correct formula is 125*[lambda]*sin(theta) = m*[lambda], with m = 1/2 for the first minimum. The resulting value for theta is 0.23 degrees.
  • #1
robera1
22
0

Homework Statement



"If the distance between the centers of adjacent slits in the five-slit mask is 125[lambda], determine the angle (measured relative to the normal to the screen) to the minimum closest to the center of the screen."

Homework Equations


So, I have a question about the homework due tomorrow.
Here is the question:

So, do I use dsin[theta] = m[lambda]?
Where d would be, well, I am not sure,
Theta is what I'd be solving for,
m would be 0.5 (I think, but not sure since there are 5 slits)
and lambda would be 125

Is this right, or totally wrong?
 
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  • #2
Correct formula. "d" is the distance between slits, so replace it with 125*L
(I'm writing L instead of lambda). That gives you
125*L*sin(A) = m*L
For the first minimum, m = 1/2.
The L cancels, so you can find A.
 
  • #3
Okay, so theta = 0.23 degrees?
 
  • #4
Yes, that's it.
 
  • #5
Awesome! Thanks :D
 

What is multiple-slit interference?

Multiple-slit interference is a phenomenon that occurs when light waves pass through multiple parallel slits and interfere with each other, resulting in a pattern of bright and dark fringes on a screen.

What is the difference between single-slit and multiple-slit interference?

In single-slit interference, light waves pass through a single slit and interfere with each other to create a diffraction pattern. In multiple-slit interference, light waves pass through multiple parallel slits and interfere with each other to create a more complex interference pattern.

What factors affect the interference pattern in multiple-slit interference?

The interference pattern in multiple-slit interference is affected by the distance between the slits, the wavelength of the light, and the angle of incidence of the light waves.

How does the number of slits affect the interference pattern in multiple-slit interference?

The number of slits affects the intensity of the interference pattern in multiple-slit interference. As the number of slits increases, the number of interference fringes also increases and the intensity of the bright fringes decreases.

How is multiple-slit interference used in practical applications?

Multiple-slit interference is used in various applications such as in optical instruments like spectrometers, in diffraction gratings for separating light into its component colors, and in anti-reflective coatings on lenses to reduce glare.

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