In a Young's double slit experiment the separation of the slits is 0.23 mm. The distance to the screen is 1.12 m. The third bright fringe is a distance of 5.9 mm from the central fringe. Determine the wavelength of the light.
Question
In a Young's double slit experiment the separation of the slits is 0.23 mm. The distance to the screen is 1.12 m. The third bright fringe is a distance of 5.9 mm from the central fringe. Determine the wavelength of the light.
Solution
Sure, here's how you can calculate the wavelength of the light in a Young's double slit experiment:
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First, we need to understand the formula that relates the variables in this experiment. The formula is: λ = (yd) / (mL), where:
λ is the wavelength of the light, y is the distance from the central fringe to the mth bright fringe, d is the separation of the slits, m is the order number of the bright fringe (m=1 for the first bright fringe, m=2 for the second, etc.), L is the distance to the screen.
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Now, we can substitute the given values into the formula:
y = 5.9 mm = 5.9 * 10^-3 m (we need to convert mm to m), d = 0.23 mm = 0.23 * 10^-3 m, m = 3 (since we're looking for the third bright fringe), L = 1.12 m.
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Substituting these values into the formula gives us:
λ = (5.9 * 10^-3 m * 0.23 * 10^-3 m) / (3 * 1.12 m) = 3.8 * 10^-7 m = 380 nm.
So, the wavelength of the light in this experiment is 380 nm.
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