Youngs double split experiment

In summary, when trying to solve for the distance between two fringes, remember to use the equation sin(theta) = (m +.5) lambda / d. The equation for destructive interference is: x = L \frac{(m+\frac{1}{2} )\lambda}{d}
  • #1
Kris1120
42
0

Homework Statement


Light of wavelength 473 nm falls on two
slits spaced 0.389 mm apart.
What is the required distance from the slit
to a screen if the spacing between the first and
second dark fringes is to be 6.71 mm?
Answer in units of m.



Homework Equations



sin[tex]\theta[/tex]= m[tex]\lambda[/tex]/d

x=tan[tex]\theta[/tex]*L

The Attempt at a Solution



[tex]\theta[/tex] = sin-1{2*473e-9m / .389e-3 m} = .139336 degrees

L = 6.71e-3 m / tan .139336 = 2.75919
 
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  • #2
Hi Kris1120,

Kris1120 said:

Homework Statement


Light of wavelength 473 nm falls on two
slits spaced 0.389 mm apart.
What is the required distance from the slit
to a screen if the spacing between the first and
second dark fringes is to be 6.71 mm?
Answer in units of m.



Homework Equations



sin[tex]\theta[/tex]= m[tex]\lambda[/tex]/d

I don't believe this is the formula you want. They are referring to the dark fringes in this problem.


Also, when you solve for the distance remember they want the distance between two fringes, not the distance from one fringe to the center point.
 
  • #3
Ok so I am using the equation sin(theta) = (m +.5) lambda / d ... Does that mean I do not use the equation to solve for x?
 
  • #4
Kris1120 said:
Ok so I am using the equation sin(theta) = (m +.5) lambda / d ... Does that mean I do not use the equation to solve for x?

You do still have to solve for x.

However, I think here you should use the small angle approximation that combines both equations (because for small enough angles sin(theta)=tan(theta)). Does your book have that formula?
 
  • #5
No. I can't find it
 
  • #6
Kris1120 said:
No. I can't find it

For constructive interference, you have the two equations that you had in your original post:

[tex]
\sin\theta= \frac{m\lambda}{d}
[/tex]

[tex]
\tan\theta= \frac{x}{L}
[/tex]

For small angles,

[tex]
\frac{x}{L} =\frac{m\lambda}{d}
[/tex]
so you can find the distance along the screen x directly for each line order (again, when the angles are small). You can do the same thing with the destructive interference case, and get the same equation with m [itex]\to[/itex] (m+1/2).
 
  • #7
If I am not misunderstanding... I set the sin equation equal to the tan equation and solve for L... I am still not getting it correct though. I am trying to look the equation up on google.
 
  • #8
Maybe I am using the wrong m... m=2?
 
  • #9
Kris1120 said:
If I am not misunderstanding... I set the sin equation equal to the tan equation and solve for L... I am still not getting it correct though. I am trying to look the equation up on google.

The formula that I mentioned for the destructive interference:

[tex]
x = L \frac{(m+\frac{1}{2} )\lambda}{d}
[/tex]

gives the x value for each fringe. What they tell you in the problem is that the difference in the x values is 6.71mm. Do you see what to do?

I just saw your last post. The first order dark fringe would have m=0, and the second order dark fringe would have m=1, based on how you wrote your destructive interference condition.
 
  • #10
6.71 mm = [L((1+.5) * 473 nm)/ .389 mm] - [L((0+.5)*473nm)/ .389 mm] and solve for L? I get L = 5.51809 m is that correct?
 
  • #11
Kris1120 said:
6.71 mm = [L((1+.5) * 473 nm)/ .389 mm] - [L((0+.5)*473nm)/ .389 mm] and solve for L? I get L = 5.51809 m is that correct?

That looks right to me.
 
  • #12
Great! Thank you for being so patient with me.
 
  • #13
I'm glad to help!
 

What is Young's double slit experiment?

The Young's double slit experiment is a classic experiment in physics that demonstrates the wave nature of light. It involves a beam of light passing through two closely spaced slits and interfering with itself to create a pattern of bright and dark fringes on a screen.

What does the Young's double slit experiment prove?

The experiment proves that light behaves as a wave, as the interference pattern created by the two slits is only possible with wave-like behavior. This experiment also helped to support the wave theory of light proposed by Thomas Young in the early 1800s.

What factors affect the interference pattern in the Young's double slit experiment?

The interference pattern is affected by the wavelength of the light, the distance between the two slits, and the distance from the slits to the screen. These factors can be adjusted to change the pattern and provide evidence for the wave nature of light.

What happens if the distance between the slits is increased in the Young's double slit experiment?

If the distance between the slits is increased, the interference pattern on the screen will become wider and the fringes will become further apart. This is because the diffraction of light increases as the distance between the slits increases, leading to a wider interference pattern.

What other applications does the Young's double slit experiment have?

The principles demonstrated in the Young's double slit experiment are not limited to light, but can also be applied to other wave-like phenomena such as sound waves and electron waves. This experiment has also been used in the development of technologies such as holography and diffraction gratings.

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