In a double-slit experiment, the distance between the slits is 0.25 mm and the screen is 2.0 m away. The second-order bright fringe is observed at a distance of 8.0 mm from the central bright fringe. What is the wavelength of the light used?
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Correct answer
A. 500 nm
Principle or equation
For constructive interference in Young's double-slit experiment, the position of the m-th bright fringe from the central maximum is given by y_m = m λ L / d, where d is slit separation, L is distance to screen, and λ is wavelength.
Why this answer is correct
Given d = 0.25 mm = 2.5 × 10^-4 m, L = 2.0 m, m = 2, y_2 = 8.0 mm = 8.0 × 10^-3 m. Solve for λ: λ = y_2 d / (m L) = (8.0 × 10^-3 × 2.5 × 10^-4) / (2 × 2.0) = 2.0 × 10^-6 / 4 = 5.0 × 10^-7 m = 500 nm.
Example
If the second bright fringe is 8.0 mm from center with d=0.25 mm and L=2.0 m, then λ=500 nm.
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