Phase difference between waves in two-slit model

In summary, the phase difference between the waves from the two slits arriving at point P in a double slit experiment is 165°. This was calculated using the equation σ / λ = ΔΦ / 2π and taking into account the distance between the slits, the wavelength, and the angular separation at point P. To convert the result to be between 0-360°, the 69 complete oscillations were ignored and the remainder was taken, resulting in 165°.
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vetgirl1990
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Homework Statement


In a double slit experiment, the distance between the slits is 0.2mm and the distance to the screen is 150cm. What is the phase difference in degrees, between the waves from the two slits arriving at point P, when the angular distance of P is 10 degrees relative to the central peak? The wavelength is 500nm. Convert your result so that the angle is between 0-360°

Answer: 165°

Homework Equations


σ / λ = ΔΦ / 2π

The Attempt at a Solution


σ = dsinθ
(dsinθ) / λ = ΔΦ / 2π

ΔΦ = (dsinθ)2π/λ = (0.00003473)2π / 5x10-7
ΔΦ = 436 rads * 180°/π = 24980°

Was it necessary to take into account the distance to the screen, since we were given angular separation? Also, I'm unsure of how to "convert the result so that the angle is between 0-360°).

EDIT: Figured this out!
If the phase shift is 436 rad, we know that the phase shift is also 69.39 oscillations, because 436/2pi = 69.46. Essentially, we can ignore the 69 complete oscillations and just focus on that .46. 436 - (2pi x 69) = 2.89. If you convert that to degrees, you get 165.
 
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Nice. Solved
 

1. What is the phase difference between waves in the two-slit model?

The phase difference between waves in the two-slit model refers to the difference in the starting point or phase of two waves that are interfering with each other. It is measured in degrees or radians and plays a crucial role in determining the resulting interference pattern.

2. How is the phase difference calculated in the two-slit model?

The phase difference can be calculated by finding the path difference between the two waves and converting it into radians or degrees. This can be done by dividing the path difference by the wavelength of the waves. The resulting value gives the phase difference between the two waves.

3. What is the significance of phase difference in the two-slit model?

The phase difference is crucial in determining the interference pattern in the two-slit model. When the phase difference is a whole number of wavelengths, constructive interference occurs and results in a bright fringe. However, when the phase difference is a half number of wavelengths, destructive interference occurs and results in a dark fringe.

4. Can the phase difference be manipulated in the two-slit model?

Yes, the phase difference can be manipulated by changing the path difference between the two waves. This can be done by changing the distance between the two slits or by changing the wavelength of the waves being used. Manipulating the phase difference can result in different interference patterns.

5. How does the phase difference affect the intensity of the interference pattern in the two-slit model?

The phase difference affects the intensity of the interference pattern by determining whether constructive or destructive interference occurs. When the phase difference is a whole number of wavelengths, constructive interference occurs, resulting in a bright fringe with high intensity. On the other hand, when the phase difference is a half number of wavelengths, destructive interference occurs, resulting in a dark fringe with low intensity.

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