Question
Find the intensity at a point on a screen in Young’s double slit experiment where the interfering waves have a path difference of (i) $\lambda/6$, and (ii) $\lambda/2.$
✓
Answer
Phase difference $=\frac{2\pi}{\lambda}\times$ Path diffrence
Path difference $\frac{\lambda}{6}$ ⟹ phase difference $=\frac{\pi}{3}$
Path difference $\frac{\lambda}{2}$ ⟹ phase difference $={\pi}$
$\text{I}=4\text{I}_0\cos^{2}\bigg(\frac{\phi}{2}\bigg)$
Path difference $\frac{\lambda}{6}$ ⟹ phase difference $=\frac{\pi}{3}$
Path difference $\frac{\lambda}{2}$ ⟹ phase difference $={\pi}$
$\text{I}=4\text{I}_0\cos^{2}\bigg(\frac{\phi}{2}\bigg)$
- $\text{I}_1=4\text{I}_0\times\frac{3}{4}=3\text{I}_0$
- $\text{I}_2=4\text{I}_0\times0=0$
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