Double Slit Diffraction Problem

In summary, the conversation discusses a problem on an exam related to the conditions for constructive interference in terms of path lengths. The individual diagrammed the problem and used Pythagorean's theorem to find the difference between two distances, and then took the arctan of that distance divided by D1. However, they were told that they over-thought the problem and that the path difference must be a whole number of wavelengths for constructive interference. The conversation also mentions the formula for the path difference between the zeroth and nth maximum and the role of D and d in the problem.
  • #1
spitonem
4
0
I had this problem on my exam and I was pretty sure i knew what to do but it couldn't come up with the right answers.
I diagrammed the problem and showed the way i tried to solve it in blue. Can someone tell me where i went wrong?
W6xA170.png


Basically i found the length the of the first maximum off the center. i used Pythagorean's theorem to find D2. Then subtracted the two distances to find the difference. I then took the arctan of that distance divided by D1.
 
Science news on Phys.org
  • #2
You way over-thought the problem.
Start from the physics: what is the condition that makes a maximum?
 
  • #3
the center of a maximum is complete constructive interference from two rays of light?
 
  • #4
the center of a maximum is complete constructive interference from two rays of light?
... good - so what is the condition for constructive interference in terms of the path lengths?
 
  • #5
wouldn't it be the wavelength plus by any integer being multiplied by the wavelength?
 
  • #6
wouldn't it be the wavelength plus by any integer being multiplied by the wavelength?
Almost: the path difference has to be a whole number of wavelengths for constructive interference.
This makes the central maximum the zeroth maximum ... with the 1st and second etc on either side of it.

Lets say D is the perpendicular distance from the slits to the screen - as it is in your diagram.
If D>>d, the path difference between the zeroth maximum and the nth maximum is ##D_n-D=d\sin\theta_n##
You've seen a formula like that before.
 

Related to Double Slit Diffraction Problem

1. What is the double slit diffraction problem?

The double slit diffraction problem is a phenomenon in which light passing through two parallel slits causes an interference pattern that cannot be explained by classical wave theory. It is one of the key experiments that led to the development of quantum mechanics.

2. What causes the double slit diffraction pattern?

The double slit diffraction pattern is caused by the wave nature of light. When light passes through two parallel slits, it diffracts and creates two coherent wavefronts that overlap and interfere with each other, resulting in a pattern of bright and dark fringes on a screen placed behind the slits.

3. How does the width of the slits affect the double slit diffraction pattern?

The width of the slits has a significant impact on the double slit diffraction pattern. As the slits become narrower, the diffraction pattern becomes wider and the fringes become closer together. This is because narrower slits cause more diffraction, resulting in a greater overlap of the two wavefronts and more pronounced interference.

4. Can the double slit diffraction pattern be observed with other types of waves?

Yes, the double slit diffraction pattern can be observed with other types of waves, such as sound waves, water waves, and even electrons. This phenomenon is not limited to light waves and can be observed with any type of wave that exhibits wave-like behavior.

5. What is the significance of the double slit diffraction problem in quantum mechanics?

The double slit diffraction problem played a crucial role in the development of quantum mechanics as it showed that the behavior of light and matter at the subatomic level cannot be explained by classical wave theory. It led to the development of the wave-particle duality concept, which states that particles can also exhibit wave-like behavior, and paved the way for further discoveries in quantum mechanics.

Similar threads

Single Slit Fraunhofer Diffraction
    • Optics
Replies
4
Views
1K
B Explanation for bright fringes in Single Slit Diffraction
    • Classical Physics
Replies
4
Views
471
Constant intensity maxima in double-slit interference ?
    • Optics
Replies
8
Views
4K
I Double-Slit Experiment: Does rate of photon emission matter?
    • Quantum Physics
Replies
16
Views
1K
Intensity - Double slit diffraction
    • Optics
Replies
1
Views
2K
Diffraction: Intensity in the double slit situation
    • Optics
Replies
2
Views
2K
Diffraction Grating Vs Double-Slit: Small angle Approx.
    • Introductory Physics Homework Help
Replies
1
Views
7K
Distance between fringes in an interference pattern?
    • Optics
Replies
4
Views
4K
Understanding Diffraction in a Double Slit Experiment
    • Optics
Replies
1
Views
2K
Double slit diffraction ripple
    • Introductory Physics Homework Help
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top