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(D) The resultant intensity $I_R$ for two interfering waves is given by the formula:$I_R = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$Given $I_1 = I$ and $

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$4I$

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(D) The resultant intensity $I_R$ for two interfering waves is given by the formula:$I_R = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$Given $I_1 = I$ and $I_2 = 4I$.For point $A$,the phase difference $\phi_A = \pi/2$:$I_A = I + 4I + 2\sqrt{I \cdot 4I} \cos(\pi/2) = 5I + 2(2I)(0) = 5I$For point $B$,the phase difference $\phi_B = 2\pi$:$I_B = I + 4I + 2\sqrt{I \cdot 4I} \cos(2\pi) = 5I + 2(2I)(1) = 5I + 4I = 9I$The difference between the resultant intensities at points $A$ and $B$ is:$|I_B - I_A| = |9I - 5I| = 4I$

Two light beams of intensities $I$ and $4I$ produce an interference pattern on a screen. If the phase difference between them at point $A$ is $\pi/2$ and at point $B$ is $2\pi$,find the difference between the resultant intensities at points $A$ and $B$.

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