Two beams of light having intensities I and 4 | vedclass

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(A) The resultant intensity $I_R$ of 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

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$5I, 9I$

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(A) The resultant intensity $I_R$ of 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 $I_2 = 4I$.At point $A$,the phase difference $\phi_A = \pi/2$:$I_A = I + 4I + 2\sqrt{I \cdot 4I} \cos(\pi/2)$Since $\cos(\pi/2) = 0$,we get:$I_A = I + 4I + 0 = 5I$At point $B$,the phase difference $\phi_B = 2\pi$:$I_B = I + 4I + 2\sqrt{I \cdot 4I} \cos(2\pi)$Since $\cos(2\pi) = 1$,we get:$I_B = I + 4I + 2(2I)(1) = 5I + 4I = 9I$Therefore,the resultant intensities at points $A$ and $B$ are $5I$ and $9I$ respectively.

Two beams of light having intensities $I$ and $4I$ interfere to produce fringes on a screen. The phase difference between the beams at point $A$ is $\pi/2$ and at point $B$ is $2\pi$. Find the resultant intensities at points $A$ and $B$.

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