Question

Sol. [Key Concept: Young's double slit — intensity I = 4I₀cos²(φ/2)] $I = I_{0}\cos^{2}\frac{\Delta\phi}{2}\left\lbrack I_{0} \rightarrow \right.\ $ maximum intensity $\rbrack$

$$\begin{matrix} & I = I_{0}\cos^{2}\frac{K\Delta x}{2} \\ & K = I_{0}\cos^{2}\left( \frac{2\pi}{\lambda} \times \frac{\lambda}{2} \right) \\ & K = I_{0} \\ & K_{1} = I_{0}\cos^{2}\left( \frac{2\pi}{\lambda} \times \frac{\lambda}{3 \times 2} \right) = I_{0}\cos^{2}\left( \frac{\pi}{3} \right) \\ & K_{1} = \frac{I_{0}}{4} \\ & \frac{K}{K_{1}} = 4 \Rightarrow K_{1} = \frac{K}{4} \end{matrix}$$