Finding the angle of phase difference - two slit model

In summary, the problem is asking for the angle at which the phase difference between the waves from two slits would be 2 radians when illuminated with light of a wavelength 548nm and with a distance of 0.25mm between the slits. This can be solved using the formula σ / λ = ΔΦ / 2π, where σ is the path difference, λ is the wavelength, and ΔΦ is the phase difference. After substituting the given values and solving for θ, we get an answer of 0.04°, which is the angle at which the phase difference would be 2 radians.
  • #1
vetgirl1990
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Homework Statement


Light of a wavelength 548nm illuminates two slits separated by 0.25mm. At what angle would one find the phase difference between the waves from two slits to be 2 rads?

Homework Equations


σ / λ = ΔΦ / 2π

σ: path difference
λ: wavelength
Δφ: phase difference

The Attempt at a Solution


Based on geometry of a two slit model, σ = dsinθ.
I thought this would be a simple substitution problem, but I'm not getting the correct answer (Answer = 0.04°), so I'm worried that I'm overlooking something.

σ / λ = ΔΦ / 2π
(dsinθ) / λ = ΔΦ / 2π
sinθ = (ΔΦ / 2π)(λ / d)
θ = sin-1(ΔΦ / 2π)(λ / d)

I converted rads to degrees: ΔΦ = 2 rad * π/180

θ = 0.000697°

I also tried making the small angle approximation (sinθ ≈ θ) , but still didn't get the right answer: θ = 0.0000122°
 
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  • #2
vetgirl1990 said:
θ = 0.000697°
The unit of the above value should be in radians, not degree.
 
  • #3
blue_leaf77 said:
The unit of the above value should be in radians, not degree.
The final answer is reported in degrees (0.04°)
 
  • #4
vetgirl1990 said:
The final answer is reported in degrees (0.04°)
Yes, I know, but the value of 0.000697 for ##\theta## should be in radians? Then convert it to degrees.
What's the value you got when calculating θ = sin-1(ΔΦ / 2π)(λ / d)?
 
  • #5
blue_leaf77 said:
Yes, I know, but the value of 0.000697 for ##\theta## should be in radians? Then convert it to degrees.
What's the value you got when calculating θ = sin-1(ΔΦ / 2π)(λ / d)?

θ = sin-1(ΔΦ / 2π)(λ / d)
= sin-1 (2rads / 2π)(5.48x10-7m / 2.5x10-4m)
= sin-1 (0.31831 * 0.002192)
= 0.03998 rads

Converting rads to degrees:
0.03998 rads * 180/π = 2.29

The answer is still wrong even when I leave it as radians until the end.
 
  • #6
vetgirl1990 said:
= sin-1 (0.31831 * 0.002192)
= 0.03998 rads
Check again the output of your calculator if it is in radians or degrees. If it's in degrees already, then you are getting the correct answer after rounding up to two figures behind the decimal.
 
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  • #7
blue_leaf77 said:
Check again the output of your calculator if it is in radians or degrees. If it's in degrees already, then you are getting the correct answer after rounding up to two figures behind the decimal.

Ah I see! sin-1 is automatically calculating my answer in degrees already. Thank you for your help and patience!
 
  • #8
vetgirl1990 said:
Thank you for your help and patience!
You are welcome.
 

FAQ: Finding the angle of phase difference - two slit model

1. What is the two-slit model and how does it relate to phase difference?

The two-slit model is a simplified version of the double-slit experiment used in physics to study the behavior of light. It involves sending a beam of light through two narrow parallel slits and observing the resulting interference pattern. The phase difference between the two slits determines the characteristics of this pattern.

2. How is the angle of phase difference measured in the two-slit model?

The angle of phase difference is measured by observing the locations of the interference fringes on a screen placed behind the slits. These fringes are created by the superposition of waves from the two slits, and the distance between them can be used to calculate the phase difference.

3. What factors affect the angle of phase difference in the two-slit model?

The angle of phase difference is primarily affected by the wavelength of the light source and the distance between the two slits. Other factors such as the intensity and polarization of the light can also have an impact.

4. How does the angle of phase difference impact the interference pattern in the two-slit model?

The angle of phase difference determines the spacing between the interference fringes on the screen. A larger phase difference will result in smaller fringe spacing, while a smaller phase difference will result in larger fringe spacing. This ultimately affects the overall pattern and visibility of the fringes.

5. Can the angle of phase difference be manipulated in the two-slit model?

Yes, the angle of phase difference can be manipulated by changing the distance between the slits or by altering the wavelength of the light source. This allows for further experimentation and observation of the resulting interference patterns.

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