Constructive Interference Eq'n

In summary, constructive interference is a phenomenon that occurs when two or more waves of the same frequency and amplitude meet and combine, resulting in a wave with a greater amplitude. The equation for constructive interference is I = I<sub>1</sub> + I<sub>2</sub> + 2√(I<sub>1</sub>I<sub>2</sub>)cos(ϕ), and it causes the amplitude of a wave to increase. Real-life examples of constructive interference include interference patterns in water waves, sound amplification in musical instruments, and the strengthening of radio signals. The phase difference between interfering waves also plays a crucial role, with maximum constructive interference occurring when the phase difference is 0 or a multiple
  • #1
baileya
22
0

Homework Statement


Derive the equation 2t=(n+1/2)(lamba/index of refraction) to show it's the correct eq'n for constructive interference on reflection. Include a diagram.


Homework Equations


2t=(n+1/2)(lambda/index of refraction)


The Attempt at a Solution


I'm not sure how you'd show it's the correct eq'n...
 
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  • #2
hi baileya! :smile:

(have a lambda: λ :wink:)
baileya said:
… Include a diagram.

I'm not sure how you'd show it's the correct eq'n...

you'd draw a diagram! :wink:

what does it show? :smile:
 

Related to Constructive Interference Eq'n

1. What is constructive interference?

Constructive interference is a phenomenon that occurs when two or more waves of the same frequency and amplitude meet and combine, resulting in a wave with a greater amplitude.

2. What is the equation for constructive interference?

The equation for constructive interference is given by I = I1 + I2 + 2√(I1I2)cos(ϕ), where I is the intensity of the resulting wave, I1 and I2 are the intensities of the two interfering waves, and ϕ is the phase difference between them.

3. How does constructive interference affect the amplitude of a wave?

Constructive interference causes the amplitude of a wave to increase, as the two waves combine to form a wave with a greater amplitude than either of the two individual waves.

4. What are some real-life examples of constructive interference?

Examples of constructive interference can be seen in various phenomena, such as the formation of interference patterns in water waves, the amplification of sound in musical instruments, and the creation of stronger radio signals through the combination of multiple waves.

5. How does the phase difference between interfering waves affect constructive interference?

The phase difference between interfering waves plays a crucial role in constructive interference. When the phase difference is 0 or a multiple of 2π, the waves are in phase and result in maximum constructive interference. On the other hand, when the phase difference is π or an odd multiple of π, the waves are out of phase and result in destructive interference.

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