In a two-slit experiment using coherent light, the distance between the slits and the screen is 1.10 m, and the distance between the slits is 0.100 mm. The first-order bright fringe is measured to be 3.40 cm from the centerline. What is the wavelength of the light?
Question
In a two-slit experiment using coherent light, the distance between the slits and the screen is 1.10 m, and the distance between the slits is 0.100 mm. The first-order bright fringe is measured to be 3.40 cm from the centerline. What is the wavelength of the light?
Solution
To solve this problem, we can use the formula for the double-slit interference pattern:
dsin(θ) = mλ
where:
- d is the distance between the slits,
- θ is the angle between the centerline and the position of the fringe,
- m is the order of the fringe, and
- λ is the wavelength of the light.
First, we need to find the angle θ. We can use the small angle approximation (sin(θ) ≈ tan(θ) ≈ θ for small θ), which is valid because the distance to the screen is much larger than the distance between the fringes.
The tangent of the angle is the opposite side (the distance from the centerline to the fringe, 3.40 cm) divided by the adjacent side (the distance from the slits to the screen, 1.10 m). So,
tan(θ) = 0.034 m / 1.10 m = 0.0309
Therefore, θ ≈ 0.0309.
Next, we can substitute the known values into the formula:
(0.100 x 10^-3 m) * sin(0.0309) = 1 * λ
Solving for λ gives:
λ = (0.100 x 10^-3 m) * sin(0.0309) / 1 = 3.09 x 10^-6 m = 609 nm
So, the wavelength of the light is approximately 609 nm.
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