Correct Option: (A) $2n\pi$

Step 1 (Formula / Governing Law & Given Data): [0.5 Mark]

In Young's Double Slit Experiment (YDSE), the condition for constructive interference (formation of a bright fringe/spot) is based on the path difference ($\Delta x$) and phase difference ($\phi$). The condition for constructive interference is given by:

$$ \Delta x = n\lambda \quad (\text{where } n = 0, 1, 2, \dots) $$

The relationship between path difference ($\Delta x$) and phase difference ($\phi$) is defined as:

$$ \phi = \frac{2\pi}{\lambda} \times \Delta x $$

Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]

Substitute the condition for constructive interference ($\Delta x = n\lambda$) into the phase difference formula:

$$ \phi = \frac{2\pi}{\lambda} \times (n\lambda) $$

Canceling the wavelength ($\lambda$) from the numerator and denominator:

$$ \phi = 2n\pi $$

Step 3 (Final Concluded Answer): [0.25 Mark]

Thus, for a bright spot to be formed, the phase difference between the two superimposing waves must be an integral multiple of $2\pi$.

Final Answer: The phase difference is $2n\pi$, which corresponds to option (A).

💡 EL10 Concept Insight: Imagine two waves starting their "up-and-down" dance at the exact same time; if they arrive at the screen after completing a whole number of full cycles, they will both be at the same peak or trough together, creating a bright spot through constructive interference.