Visualizing Double-Slit Interference on a Shoestring

Abstract

Student misconceptions of the double-slit experiment (Fig. 1) are abundant. The most common ones that we observe include: (1) belief that constructive interference requires both pathlengths to be integer multiples of the wavelength (“ L1 = n1λ” and “ L2 = n2λ”) rather than only the pathlength difference (Δ L ≡ | L1 – L2| = nλ); (2) failure to understand that the justification for d sin θ = nλ is that d sin θ is a good approximation to Δ L; (3) confusion about the limits in which the approximation d sin θ = nλ is valid; and (4) confusion about the limits in which the approximation sin θ = tan θ = y/ D is valid. Most of these misconceptions have been observed in the past. We consider the first of these to be the most damaging, since it will hinder students from understanding interference in other contexts in the future. To address this misconception, we have designed an exercise that strongly reinforces the correct understanding (Δ L = nλ) while also helping overcome the other misconceptions.