YDSE Phase Difference and Central Fringe – Rankers Physics

Young's Double Slit Experiment: Practice Problem & Solution

Assertion (A): If the phase difference between the light waves emerging from the slits of the Young's experiment is \(\pi\) radian, then central fringe will be dark. Reason (R): Phase difference is equal to \(\frac{2\pi}{\lambda}\) times the effective path difference.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Young's Double Slit Experiment. Understanding the underlying formula is key to arriving at the correct answer below:

Assertion (A) is true. An initial \(\pi\) phase difference means destructive interference at the central point (where path difference is zero). Reason (R) is also true, as \(\Delta\phi = \frac{2\pi}{\lambda} \Delta x). (R) explains how phase difference relates to path difference, justifying (A).

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