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(C) The resultant intensity $I_R$ in an interference pattern is given by the formula: $I_R = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$,where $\phi$ is th

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$6$

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(C) The resultant intensity $I_R$ in an interference pattern is given by the formula: $I_R = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$,where $\phi$ is the phase difference.Given $I_1 = I$ and $I_2 = 9I$.At point $P$,the phase difference $\phi_P = \pi / 2$. Thus,$I_P = I + 9I + 2\sqrt{I \cdot 9I} \cos(\pi / 2) = 10I + 6I(0) = 10I$.At point $Q$,the phase difference $\phi_Q = \pi$. Thus,$I_Q = I + 9I + 2\sqrt{I \cdot 9I} \cos(\pi) = 10I + 6I(-1) = 10I - 6I = 4I$.The difference between the resultant intensities at points $P$ and $Q$ is $|I_P - I_Q| = |10I - 4I| = 6I$.

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