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Define path difference

Path difference is the difference between the distances travelled by two waves from their sources to the same observation point. For in-phase coherent sources, it determines whether the waves arrive in phase or out of phase.

Apply the conditions

Constructive interference occurs when path difference $=n\lambda$ . Destructive interference occurs when path difference $=(n+\tfrac12)\lambda$ , where $n$ is a whole number.

Count fringes carefully

Start from the central bright fringe when the path difference is zero. Each additional bright fringe changes the path difference by $\lambda$ ; dark fringes lie halfway between adjacent bright conditions.

Common trap

Do not assign $\lambda/2$ to every dark point. The first dark condition is $\lambda/2$ , then $3\lambda/2$ , $5\lambda/2$ , and so on.

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In a double-slit experiment using coherent light of wavelength $\lambda$ , the central bright fringe is observed on a screen at point P. A point of destructive interference occurs at point Q. Only one point of constructive interference is observed between P and Q.

What is the path difference at Q ?

C.3 Wave phenomena is secure when you can connect the physical picture to the equation and its limits.

Wavefronts and rays
Reflection, refraction and Snell’s law
Refractive index and total internal reflection
Superposition, coherent sources and interference
Young’s double-slit pattern

C.3.7—Path difference

Use Path Difference for Interference

Retrieve the Core C.3 Wave Phenomena Model

C.3.7 Exam Analysis