First slide

Coherent sources

Question

A source emits electromagnetic waves of wavelength 3 m. One beam reaches the observer directly and other after reflection from a water surface, travel ling 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

Moderate

A

$(1 / 4)$ fold
B

$(3 / 4)$ fold
C

$(5 / 4)$ fold
D

$(9 / 4)$

Solution

We know that a phase change of $π$ occurs when the reflection takes place at the boundary of denser medium. This is equivalent to a path difference of $λ / 2 .$
Total phase difference $= π - π = 0$
Thus the two waves superimpose in phase.
Resultant amplitude $= \sqrt{I} + \sqrt{(I / 4)} = 3 / 2 \cdot \sqrt{1}$
Resultant intensity
$= {(\frac{3}{2} \sqrt{I})}^{2} = \frac{9}{4} I = \frac{9}{4} fold$

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