Two coherent sources of light interfere and produce fringe patterns on a screen. For the central maximum, the

Question

Two coherent sources of light interfere and produce fringe patterns on a screen. For the central maximum, the phase difference between the two waves will be:

Accepted Answer

1. **Condition for Constructive Interference:** Constructive interference (bright fringes or maxima) occurs when the phase difference ($\phi$) between the two interfering waves is an even integral multiple of $\pi$. Mathematically, $\phi = 2n\pi$, where $n = 0, 1, 2, \dots$.
2. **Central Maximum:** The central maximum corresponds to the geometric center of the fringe pattern where the path difference ($\Delta x$) between the waves from the two coherent sources is zero.
3. **Phase Difference Calculation:** The relationship between phase difference and path difference is given by $\phi = \frac{2\pi}{\lambda} \Delta x$. For the central maximum, since $\Delta x = 0$, the phase difference $\phi = 0$.
4. **Conclusion:** Therefore, for the central maximum, the phase difference is zero.

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