1. The problem statement, all variables and given/known data The centres of two slits of width a are a distance d apart. If the fourth minimum of the interference pattern occurs at the location of the first minimum of the diffraction pattern for light, the ratio a/d is equal to: ANS: 1/4 2. Relevant equations Here are the various interference conditions for interference and diffraction: Interference conditions for double slit: MAX: dsinθ = mλ MIN: dsinθ = (m+½)λ Diffraction conditions for a single slit: MAX: asinθ = (m+½)λ MIN: asinθ = mλ Diffraction conditions for diffraction grating: MAX: asinθ = mλ MIN: asinθ = (m+½)λ 3. The attempt at a solution I will walk through my reasoning... I've classified the diffraction component of this problem as diffraction grating rather than diffraction through a single slit, because based on this setup, there are two slits for diffraction to occur through. While we normally see grating in the order of 2500grates/cm, 2grates/cm would still be considered grating. So based on that logic, the conditions for minimum for both are: Diffraction: dsinθ = (m+½)λ, where m=1 Interference: asinθ = (m+½)λ, where m=4 Now, when I plug in all the values for m, and cancel out all the similarities (sinθ, λ): asinθ=(1+½)λ --> a=1.5 dsinθ=(4+½)λ --> d=4.5 The ratio I get for a/d = 1.5/4.5 = ⅓ HOWEVER, I noticed that if I cancel out ½ rather than adding it to m like I did above, then the ratio for a/d=¼. What am I doing wrong?