In a double-slit interference pattern, the third maximum from the central maximum corresponds to which value of m?
A) 1
B) 2
C) 3
D) 4
E) 5

Question

Quizplus · Accepted Answer

The distance between the central maximum and the third maximum in a double-slit interference pattern is given by d sin θ = 3λ/2, where d is the distance between the slits, θ is the angle between the line from the center of the screen to the third maximum and a line perpendicular to the screen, and λ is the wavelength of light used in the experiment. The third maximum occurs when the path difference between the waves from the two slits is 3λ/2. Using the formula for path difference, we can write this as d sin θ = 3λ/2. Rearranging the formula, we get sinθ = (3λ/2)/d. Using the small angle approximation, we can write sinθ ≈ θ, so we get θ ≈ (3λ/2)/d. Using the formula for the position of the maxima in a double-slit interference pattern, we can write sinθ = mλ/d, where m is an integer that represents the order of the maximum (m = 0 for the central maximum, m = +/- 1 for the first order maxima, m = +/- 2 for the second order maxima, etc.). Equating the two expressions for sinθ, we get mλ/d ≈ (3λ/2)/d, which simplifies to m ≈ 3/2. Since m must be an integer, the only possible value is m = 2 for the third maximum. Therefore, the answer is B) 2.

In a Double-Slit Interference Pattern, the Third Maximum from the Central