Interference in a Double-Slit Experiment

In summary, the double-slit experiment involves a distance of 5.0mm between slits and a distance of 1.0m from the screen. The two interference patterns on the screen are caused by light of wavelengths 480nm and 600nm. To find the separation between the third-order bright fringes of the two patterns, the equation $d\sin\theta=m\lambda$ can be used, but values of $\theta$ are needed. A drawing of the situation and the positions of the fringes can help determine these values.
  • #1
annikaw
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In a double-slit experiment, the distance between slits is 5.0mm and the slits are 1.0m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 480nm, and the other due to light of wavelength 600nm. What is the separation on the screen between the third-order (m=3) bright fringes of the two interference patterns?

From my notes, I find that $d\sin\theta=m\lambda$.

However, I do not know how to get values of $\theta$ that can be put to the equation to find the difference in separation.
 
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  • #2
annikaw said:
In a double-slit experiment, the distance between slits is 5.0mm and the slits are 1.0m from the screen. Two interference patterns can be seen on the screen: one due to light of wavelength 480nm, and the other due to light of wavelength 600nm. What is the separation on the screen between the third-order (m=3) bright fringes of the two interference patterns?

From my notes, I find that $d\sin\theta=m\lambda$.

However, I do not know how to get values of $\theta$ that can be put to the equation to find the difference in separation.

Hi annikaw! Welcome to MHB! (Smile)

Let's get a drawing of the situation:
View attachment 4506

We get a bright fringe when $d\sin\theta=m\lambda$.
The corresponding position on the screen is $OP=D\sin\theta$.

Can you deduce where the 2 requested fringes are?
 

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Related to Interference in a Double-Slit Experiment

1. What is interference in a double-slit experiment?

Interference in a double-slit experiment is a phenomenon where two waves, such as light or sound waves, overlap and interact with each other, resulting in a pattern of alternating bright and dark regions. This pattern is caused by the constructive and destructive interference of the waves.

2. How is interference observed in a double-slit experiment?

In a double-slit experiment, a beam of particles or waves is directed towards two parallel slits. As the particles or waves pass through the slits, they spread out and create a pattern on a screen behind the slits. This pattern is the result of the interference of the particles or waves as they pass through the slits and interact with each other.

3. What causes interference in a double-slit experiment?

The interference observed in a double-slit experiment is caused by the superposition of waves. When two or more waves meet at a point, they combine and create a new wave. This new wave can have a larger or smaller amplitude than the individual waves, depending on whether the waves are in phase (constructive interference) or out of phase (destructive interference).

4. What is the significance of interference in a double-slit experiment?

The interference observed in a double-slit experiment is significant because it demonstrates the wave-like nature of particles, such as photons or electrons. It also provides evidence for the concept of superposition, where two or more waves can combine to create a new wave with a different amplitude. This phenomenon has implications in various fields, including quantum mechanics and optics.

5. How does the distance between the slits affect interference in a double-slit experiment?

The distance between the two slits in a double-slit experiment plays a crucial role in the interference pattern observed. As the distance between the slits increases, the interference pattern becomes more spread out, resulting in a larger distance between the bright and dark fringes. On the other hand, a smaller distance between the slits leads to a more tightly packed interference pattern. This relationship is known as the "interference fringe spacing."

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