In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 22 micrometers. At what angle away from the centerline does the first bright fringe occur?
Question
In a two-slit experiment, monochromatic coherent light of wavelength 600 nm passes through a pair of slits separated by 22 micrometers. At what angle away from the centerline does the first bright fringe occur?
Solution
The angle of the first bright fringe in a two-slit experiment can be calculated using the formula for constructive interference:
θ = arcsin(mλ/d)
where:
- m is the order of the fringe (m = 1 for the first bright fringe),
- λ is the wavelength of the light, and
- d is the separation of the slits.
Given that λ = 600 nm = 600 x 10^-9 m and d = 22 µm = 22 x 10^-6 m, we can substitute these values into the formula:
θ = arcsin((1 * 600 x 10^-9 m) / (22 x 10^-6 m))
Solving this will give you the angle θ in radians. To convert to degrees, multiply by (180/π).
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