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JIPMER 2017
Exam
JIPMER
Year
2017
Subject
Physics
Chapter
Wave Optics

JIPMER 2017 · Physics · Wave Optics

A source emits electromagnetic waves of wavelength 3 m . One beam...

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 1/41 / 4 as compared to intensity due to the direct beam alone. The resultant intensity will be

Options

  1. A(1/4) fold
  2. B(3/4) fold
  3. C(5/4) fold
  4. D(9/4) fold

Correct answer

D. (9/4) fold

Step-by-step solution

We know that a phase change of π\pi occurs when the reflection takes place at the boundary of denser medium. This is equivalent to a path difference of λ/2\lambda / 2. ∴\therefore Total phase difference =π−π=0=\pi-\pi=0 Thus, the two waves superimpose in phase.  Resultant amplitude =I+(I4)=32I Resultant intensity =(32I)2=94I=94 fold. \begin{aligned} & \text{ Resultant amplitude }=\sqrt{I}+\sqrt{\left(\frac{I}{4}\right)}=\frac{3}{2} \sqrt{I} \\ & \text{ Resultant intensity }=\left(\frac{3}{2} \sqrt{I}\right)^2=\frac{9}{4} I=\frac{9}{4} \text{ fold. } \end{aligned}
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