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  4. The equations of two interfering waves are y1=b cos ω t and y2=b cos (ω t+φ) . For destructive interference the path difference is

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Q. The equations of two interfering waves are $y_{1}=b \cos \omega t$ and $y_{2}=b \cos (\omega t+\phi) .$ For destructive interference the path difference is

Wave Optics

Solution:

For destructive interference, path difference $=\frac{\lambda}{2}$.
Therefore, phase difference $=\frac{2 \pi}{\lambda} \cdot \frac{\lambda}{2}=\pi$ radian $=180^{\circ}$.