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Wave Optics
Interference of Waves
1 question from 1 paper, each with its answer.
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- paper
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- of Wave Optics
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Concepts tested
- Maximum and minimum intensity in superposition
All Questions
2008 AIPMT 1 question
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Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is -Resultant intensity for a phase difference $\phi$: $I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi$
Maximum intensity ($\cos\phi = +1$): $I_{max} = I_1 + I_2 + 2\sqrt{I_1 I_2} = (\sqrt{I_1} + \sqrt{I_2})^2$
Minimum intensity ($\cos\phi = -1$): $I_{min} = I_1 + I_2 - 2\sqrt{I_1 I_2} = (\sqrt{I_1} - \sqrt{I_2})^2$
$I_{max} + I_{min} = (\sqrt{I_1} + \sqrt{I_2})^2 + (\sqrt{I_1} - \sqrt{I_2})^2$
$= (I_1 + I_2 + 2\sqrt{I_1 I_2}) + (I_1 + I_2 - 2\sqrt{I_1 I_2})$
$= 2(I_1 + I_2)$