A source emits electromagnetic waves of wavelength 3 m. One beam reaches the observer directly and other after reflection from a water surface, travelling 1.5 m extra distance and with intensity reduced to 1/4 as compared to intensity due to the direct beam alone. The resultant intensity will be

$$\begin{gathered} We know that a phase change of \pi occurs when the reflection take place \\ at the boundary of denser medium. \\ Due to geometry, \\ ∆{\varphi }_1 = \frac{2\pi }{\lambda }∆x \\ =\frac{2\pi }{3}\left(1.5\right)=\pi radian. \\ Due to phase change, \\ ∆{\varphi }_2 = \pi radian \\ \therefore Total phase difference of second wave \\ when it reached the observer \\ ∆\varphi =∆{\varphi }_1+∆{\varphi }_2=2\pi radian \\ Resul\tan t intensity = I_1+I_2+2\sqrt{I_1{I}_2}\cos \varphi \\ =I+\frac{I}{4}+2.\frac{I}{2}\cos \left(2\pi \right)=\frac{5I}{4}+I=\frac{9I}{4} \end{gathered}$$