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Two waves of same frequency and same amplitude from two monochromatic sources are allowed to superpose at a certain point. If in one case the phase difference is \mathrm{0^{\circ}} and in other case is \mathrm{\pi / 2,} the ratio of the intensities in the two cases will be:

Option: 1

1 : 1


Option: 2

2 : 1


Option: 3

4 : 1


Option: 4

none of these


Answers (1)

best_answer

From \mathrm{I_R=I_1+I_2+2 \sqrt{I_1 I_2} \cos \phi}

When \mathrm{\phi=0^{\circ}, \mathrm{I}_{\mathrm{R}}=\mathrm{I}+\mathrm{I}+2 \sqrt{\mathrm{II}} \cos 0^{\circ}=4 \mathrm{I}}

When \mathrm{\phi=90^{\circ}, I_R^{\prime}=I+I+2 \sqrt{I I} \cos 90^{\circ}=2 \mathrm{I}}

\mathrm{ \therefore \frac{\mathrm{I}_{\mathrm{R}}}{\mathrm{I}_{\mathrm{R}}^{\prime}}=\frac{4 \mathrm{I}}{2 \mathrm{I}}=2: 1 }

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