Calculating Interference Pattern Intensity for Double-Slit Experiment

In summary, the conversation discusses the use of the equation I=Imaxcos^2(pie(d)sintheta/wavelength to calculate the fraction of maximum intensity at a specific point in an interference pattern. The correct equation is given and the importance of correctly converting units is emphasized. The value for theta can also be found using the equation \sin\theta = \frac{y}{D}.
  • #1
Honda47
6
0
Two slits are separated by 0.180 mm. An interference pattern is formed on a screen 80.0 cm away by 656.3-nm light. Calculate the fraction of the maximum intensity 0.600 cm above the central maximum

I was using the equation I=Imaxcos^2(pie(d)sintheta/wavelength and I don't seem to be getting anywhere is there another equation because this one doesn't seem right and it's the only one in the chapter...
 
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  • #2
You are indeed using the right equation. But you are probably getting stuck trying to find [itex]\theta[/itex]. The intensity as a function of the phase [itex]\Delta\phi[/itex] is:

[tex]I = I_{max}\cos^2\frac{\Delta\phi}{2}[/itex]

Now, [itex]\Delta\phi = \frac{2\pi}{\lambda}\Delta x[/itex]

This should see you through...you don't need to compute [itex]\theta[/itex] if you observe that

[itex]d\sin\theta[/itex] = Path difference = [itex]\Delta x[/itex]

Cheers
Vivek
 
  • #3
Looks like the correct equation except that you do not have a closing parenthesis. Make sure you have the units right. You have mm, cm, and nm in the problem. Are you making the necessary conversions?
 
  • #4
OOps..I didn't see you have the y-coordinate of the fringe as well...in that case, for small theta,

[itex]\sin\theta = \frac{y}{D}[/itex] and that should do it.
 

Related to Calculating Interference Pattern Intensity for Double-Slit Experiment

1. What is double-slit interference?

Double-slit interference is a phenomenon in which a single beam of light passing through two narrow slits produces a pattern of light and dark bands on a screen. This occurs due to the wave-like nature of light, where the beams from the two slits interfere with each other constructively or destructively, creating the band pattern.

2. How does double-slit interference support the wave theory of light?

Double-slit interference provides evidence for the wave theory of light because the pattern produced is characteristic of wave interference. Additionally, the pattern becomes more distinct when the distance between the slits is decreased, further supporting the wave nature of light.

3. Can double-slit interference occur with other types of waves?

Yes, double-slit interference can occur with other types of waves, such as water waves and sound waves. This is because all waves exhibit similar properties, including diffraction and interference.

4. What happens when the width of the slits is increased in double-slit interference?

When the width of the slits is increased, the interference pattern becomes less defined and the bands become wider. This is because wider slits allow for more diffraction, resulting in less precise interference.

5. How is double-slit interference used in scientific research?

Double-slit interference is used in various fields of research, including optics, quantum mechanics, and material science. It has been used to study the wave nature of particles and to create precise measurements and patterns in nanotechnology. It also plays a crucial role in the development of new technologies, such as the double-slit electron microscope.

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