Two light waves of intensities I and 21 superimpose on each other, If the path difference between the light…

Two light waves of intensities I and 21 superimpose on each other, If the path difference between the light waves reaching a point is $12.5 \%$ of the wavelength of the light, then the resultant intensify at the point is (Both the light waves have same wavelength)
  1. I
  2. 9 I
  3. 3 I
  4. 5 I

Solution

For light waves, $\mathrm{I}_1=\mathrm{I}, \mathrm{I}_2=2 \mathrm{I}, \Delta \mathrm{x}=\frac{12.5}{100} \lambda=\frac{\lambda}{8}$ $\therefore$ Phase different, $\phi=\frac{2 \pi}{\lambda} \cdot \Delta x=\frac{2 \pi}{\lambda} \cdot \frac{\lambda}{8}=\frac{\pi}{4}$ $\begin{aligned} & \therefore \mathrm{I}_{\mathrm{R}}=\mathrm{I}_1+\mathrm{I}_2+2 \sqrt{\mathrm{I}_1 \mathrm{I}_2} \cos \phi \\ & =\mathrm{I}+2 \mathrm{I}+2 \sqrt{(\mathrm{I})(2 \mathrm{I})} \cos \frac{\pi}{4} \\ & =5 \mathrm{I} \end{aligned}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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