Can you please explain further because I don't understand?
Posted by Mary on Wednesday, November 14, 2007 at 4:23pm.
A wavelength of 625 nm is used in a Young's double-slit experiment. The separation between the slits is d = 1.3 10-5 m. The total width of the screen is 0.20 m. In one version of the setup, the separation between the double slit and the screen is LA = 0.35 m, whereas in another version it is LB = 0.60 m. On one side of the central bright fringe, how many bright fringes lie on the screen in the two versions of the setup? Do not include the central bright fringe in your counting. Verify that your answers are consistent with your answers to the Concept Questions.
bright fringes on one side (version A)
bright fringes on one side (version B)
For Further Reading
Physic please help! - bobpursley, Wednesday, November 14, 2007 at 6:36pm
I think it is asking you for n when x is .20 on each screen.
To solve this problem, we need to understand the concept of interference in Young's double-slit experiment.
In the double-slit experiment, light waves from two closely spaced slits interfere with each other, creating a pattern of bright and dark fringes on a screen located some distance away. The positions of these fringes can be determined using the formula:
\(y = \frac{m \lambda L}{d}\)
Where:
- \(y\) is the position of the fringe on the screen,
- \(m\) is the order of the fringe (an integer),
- \(\lambda\) is the wavelength of the light used,
- \(L\) is the distance between the double slit and the screen,
- \(d\) is the separation between the slits.
Now, let's answer the specific questions in the problem:
1. In version A, the separation between the double slit and the screen is \(L_A = 0.35\) m. We are asked to find the number of bright fringes on one side of the central bright fringe. Let's denote this number as \(n_A\).
To find \(n_A\), we need to substitute the given values into the formula and solve for \(m\):
\(0.2 = m \cdot (625 \times 10^{-9}) \cdot 0.35 / (1.3 \times 10^{-5})\)
Simplifying the equation gives:
\(0.2 = 26.9038m\)
Solving for \(m\) gives:
\(m = 0.2 / 26.9038 = 0.00744\)
Since \(m\) must be an integer, we can round \(m\) to the nearest whole number, which gives us \(m = 0\).
Therefore, in version A, there are no bright fringes on one side of the central bright fringe.
2. In version B, the separation between the double slit and the screen is \(L_B = 0.60\) m. We are asked to find the number of bright fringes on one side of the central bright fringe. Let's denote this number as \(n_B\).
Using the same formula as above, we can substitute the given values:
\(0.2 = m \cdot (625 \times 10^{-9}) \cdot 0.60 / (1.3 \times 10^{-5})\)
Simplifying the equation gives:
\(0.2 = 48.6488m\)
Solving for \(m\) gives:
\(m = 0.2 / 48.6488 = 0.00411\)
Since \(m\) must be an integer, we can round \(m\) to the nearest whole number, which gives us \(m = 0\).
Therefore, in version B, there are no bright fringes on one side of the central bright fringe.
To verify our answers, we can also refer to the concept questions. If we remember that the formula for fringe spacing (\(y\)) is proportional to the separation between the double slit and the screen (\(L\)), we can see that in both versions A and B, the separation is quite large compared to the wavelength of light used. This means that the fringes will be very close together or even overlapping, resulting in no additional bright fringes on either side of the central bright fringe.
I hope this explanation helps you understand how to solve this problem.