Light (Constructive/Destructive Interference)

In summary, the equations dsinθ=mλ and d(ym)/L=mλ represent constructive interference, while the equations dsinθ=(m+1/2)λ and d(ym)/L=(m+1/2)λ represent destructive interference. However, in the case of thin film interference, the equations 2t=mλ and 2t=(m+1/2)λ can represent both constructive and destructive interference, depending on the situation and the values of d, m, and λ. The presence of a phase shift can also affect which equation represents constructive or destructive interference.
  • #1

Homework Statement


This is not a homework question but I would like if someone could explain to me when to consider what equation constructive/destructive? I learned these two equations very vaguely in class:
dsinθ = mλ or d(ym)/L=mλ
dsinθ = (m+1/2)λ or d(ym)/L = (m+1/2)λ

The power point provided for us in class says that dsinθ=mλ is constructive and the other eqn is destructive. However when we started discussing thin film interference, suddenly the equations turned to
2t = mλ
2t= (m+1/2λ)

and in some situations 2t = mλ an equation for destructive interference and vice versa. When do I also know which equation to use for specific situations?

Homework Equations


dsinθ = mλ or d(ym)/L=mλ
dsinθ = (m+1/2)λ or d(ym)/L = (m+1/2)λ
2t = mλ
2t= (m+1/2λ)

The Attempt at a Solution

 
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  • #2
For the thin film case, the light passes twice through the film, first as the incident ray and then as the reflected ray, so the time delay is doubled.
 
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Likes Vanessa Avila
  • #3
Vanessa Avila said:

Homework Statement


This is not a homework question but I would like if someone could explain to me when to consider what equation constructive/destructive? I learned these two equations very vaguely in class:
dsinθ = mλ or d(ym)/L=mλ
dsinθ = (m+1/2)λ or d(ym)/L = (m+1/2)λ

The power point provided for us in class says that dsinθ=mλ is constructive and the other eqn is destructive.

The equations have no meaning without description of the situation, and definition of the symbols. So, what was that representation about, and what are d, m, λ, and θ?

Vanessa Avila said:
However when we started discussing thin film interference, suddenly the equations turned to
2t = mλ
2t= (m+1/2λ)

and in some situations 2t = mλ an equation for destructive interference and vice versa. When do I also know which equation to use for specific situations?

Again, what is the situation and what are d, m, λ?
 
  • #4
ehild said:
The equations have no meaning without description of the situation, and definition of the symbols. So, what was that representation about, and what are d, m, λ, and θ?
Again, what is the situation and what are d, m, λ?

d is the distance, m is the number that represents dark spots/bright spots(?), and λ is wavelength.
 
  • #5
tech99 said:
For the thin film case, the light passes twice through the film, first as the incident ray and then as the reflected ray, so the time delay is doubled.
So this phase shift changes which equation is constructive and which is destructive?
 
  • #6
Vanessa Avila said:
d is the distance, m is the number that represents dark spots/bright spots(?), and λ is wavelength.
distance of what from what? And what is θ?
 

1. What is constructive interference?

Constructive interference is when two or more waves combine to create a larger amplitude. This occurs when the crests of two waves align and add together, resulting in a stronger and more intense wave.

2. How does destructive interference differ from constructive interference?

Destructive interference is when two or more waves combine to cancel each other out. This occurs when the crests of one wave align with the troughs of another wave, resulting in a decrease in amplitude and sometimes complete cancellation of the wave.

3. What factors affect the degree of interference?

The degree of interference can be affected by factors such as the wavelength, amplitude, and phase difference between the interfering waves. The medium through which the waves are traveling can also play a role in the degree of interference.

4. What is the difference between interference and diffraction?

Interference is the result of two or more waves interacting with each other in a specific way, while diffraction is the bending of waves around obstacles or through small openings. Interference requires at least two waves, while diffraction can occur with just one wave.

5. How is the principle of interference used in everyday applications?

The principle of interference is used in many everyday applications, such as in noise-cancelling headphones, where sound waves are intentionally interfered with to cancel out unwanted noise. It is also used in the production of holograms and in various optical devices such as interferometers and spectrometers.

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