A double-slit (Young experiment) problem

In summary, the conversation discusses Young's double-slit interference experiment and finding the possible values of Φ for destructive interference at a specific point on the screen. Two different methods are used, resulting in Φ = 2kπ + 5π/4 and Φ = 2kπ - π/4. The conversation also mentions the importance of equating the cosine term to zero in order to satisfy the condition of E=0 at all times for destructive interference.
  • #1
physicist10
17
0

Homework Statement



In Young's double-slit interference experiment with light of wavelength [tex]\lambda[/tex], two light waves come from the slits and are superposed at the point P on the screen. These waves have the following forms:

E1 = E0 sin(wt + π/4)
E2 = E0 sin(wt + Φ)

Find the possible values of Φ if we have destructive interference at the point P.

Homework Equations



27baa5fb481ec2dcaf6cbb38b56f2570.png


The Attempt at a Solution



I attempted the problem two different ways and I had two different results.

Φ = 2kπ - π/4
Φ = 2kπ + 5π/4

Help me out please.
 
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  • #2
Can you show us how you got that?
 
  • #3
Phase difference is Φ - π/4.

So d/λ = (Φ - π/4)/2π

d = (2k+1)/2 λ for destructive interference

So, (2k+1)/2 λ = (Φ - π/4)/2π λ

Φ = 2kπ + 5π/4

-------------

The second way, I added 2 wave functions together and I equated the expression to zero.

I found Φ = 2kπ - π/4
 
  • #4
How did you arrive at Φ = 2kπ - π/4?
 
  • #5
Let's see. The sum of the two waves is:

E = 2E0 sin(wt + π/8 + Φ/2) cos(π/8 - Φ/2) = 0

That is satisfied when

wt + π/8 + Φ/2 = kπ

wt=2πft=2π, so we can drop it.

Φ = 2kπ - π/4
 
  • #6
physicist10 said:
Let's see. The sum of the two waves is:

E = 2E0 sin(wt + π/8 + Φ/2) cos(π/8 - Φ/2) = 0

That is satisfied when

wt + π/8 + Φ/2 = kπ

wt=2πft=2π, so we can drop it.

Φ = 2kπ - π/4

The condition E=0 must be satisfied at ALL TIME for destructive pattern, and the bold line is not true at all time.
Find another condition :wink:
 
  • #7
Hmm, thanks hikaru. How can I proceed? I have no idea.
 
  • #8
What about cos(π/8 - Φ/2)?
 
  • #9
Oh yes, I found it now. I must equate the cosine term (cos(π/8 - Φ/2)) to zero. But why exactly?
 
  • #10
Because of this: "The condition E=0 must be satisfied at ALL TIME for destructive pattern" :wink:
 

1. What is the double-slit experiment?

The double-slit experiment, also known as the Young experiment, is a classic experiment in physics that demonstrates the wave-particle duality of light. It involves shining a beam of light through two small slits and observing the interference pattern that is created on a screen behind the slits.

2. What is the purpose of the double-slit experiment?

The purpose of the double-slit experiment is to demonstrate the wave-like behavior of light. By observing the interference pattern created by the two slits, we can see that light behaves like a wave, as it demonstrates properties such as diffraction and interference.

3. How does the double-slit experiment relate to quantum mechanics?

The double-slit experiment is often used to demonstrate the principles of quantum mechanics, as it shows that particles, such as photons of light, can exhibit both wave-like and particle-like properties. This led to the development of the wave-particle duality theory in quantum mechanics.

4. What are some real-world applications of the double-slit experiment?

The double-slit experiment has been used in various fields, such as optics, quantum mechanics, and even biology. In optics, it is used to study the properties of light and in quantum mechanics, it is used to teach the principles of wave-particle duality. In biology, it has been used to study the diffraction of DNA.

5. What are some variations of the double-slit experiment?

There are many variations of the double-slit experiment, such as using different types of particles, such as electrons or protons, instead of light. It can also be performed with multiple slits, creating more complex interference patterns. Another variation is the delayed-choice experiment, which explores the concept of wave-function collapse in quantum mechanics.

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