Answer :
Final answer:
The condition for the 7th dark fringe is a phase difference of 14π and a path difference of 7λ, which accounts for an odd multiple of half wavelengths path difference leading to destructive interference.
Explanation:
The condition for getting the 7th dark fringe on the screen in terms of phase difference and path difference is a phase difference of 14π and a path difference of 7λ. Dark fringes occur when the path difference between the two waves is an odd multiple of half wavelengths, i.e., (m + ½)λ, where m is an integer. Since we are looking for the 7th dark fringe, we should substitute m=6 (as dark fringes start from m=0), giving us the condition as (6 + ½)λ = 7λ/2. Since each λ path difference corresponds to a 2π phase shift, the phase difference would be 7λ/2 × (2π/λ) = 7π. Therefore, the correct condition for the 7th dark fringe is a phase difference of 14π (since it is the 7th dark and phase difference doubles) and path difference of 7λ.
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