Question

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

• A. $\left(\frac{1}{4}\right)$ fold
• B. $\left(\frac{3}{4}\right)$ fold
• C. $\left(\frac{5}{4}\right)$ fold
• D. $\left(\frac{9}{4}\right)$ fold

Answer 1

The correct option is D $\left(\frac{9}{4}\right)$ fold

We know that a phase change of $\pi$ occurs when the reflection takes place at the boundary of denser medium. This is equivalent to a path difference of $\lambda /2$
$\therefore$ Total phase difference $=\pi -\pi =0$
Thus, the two waves superimpose in phase.
Resultant amplitude$=\sqrt{I}+\sqrt{\left(\frac{I}{4}\right)}=\frac{3}{2}\sqrt{I}$
Resultant intensity$={\left(\frac{3}{2}\sqrt{I}\right)}^2=\frac{9}{4}I=\frac{9}{4}$fold.