High School

What is the condition for getting the 7th dark fringe on the screen in terms of phase difference and path difference?

A. Phase difference of \(14\pi\) and path difference of \(\lambda/2\)
B. Phase difference of \(7\pi\) and path difference of \(\lambda\)
C. Phase difference of \(\pi/7\) and path difference of \(7\lambda\)
D. Phase difference of \(2\pi\) and path difference of \(\lambda/4\)

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.

Learn more about Constructive and Destructive Interference here:

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