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(B) The intensity at any point in an interference pattern is given by $I = I_{max} \cos^2 \left( \frac{\phi}{2} \right)$,where $\phi$ is the phase dif

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$1 : 2$

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(B) The intensity at any point in an interference pattern is given by $I = I_{max} \cos^2 \left( \frac{\phi}{2} \right)$,where $\phi$ is the phase difference.Given the path difference $\Delta = \frac{\lambda}{4}$,the phase difference is $\phi = \frac{2\pi}{\lambda} \Delta = \frac{2\pi}{\lambda} \left( \frac{\lambda}{4} \right) = \frac{\pi}{2}$.The intensity at this point is $I = I_{max} \cos^2 \left( \frac{\pi/2}{2} \right) = I_{max} \cos^2 \left( \frac{\pi}{4} \right) = I_{max} \left( \frac{1}{\sqrt{2}} \right)^2 = \frac{I_{max}}{2}$.At the central fringe,the path difference is $0$,so the intensity is $I_{max}$.Thus,the ratio of the intensity at this point to the intensity at the central fringe is $\frac{I_{max}/2}{I_{max}} = \frac{1}{2}$ or $1:2$.

The path difference between two interfering waves of equal intensities at a point on the screen is $\frac{\lambda}{4}$. The ratio of intensity at this point and that at the central fringe will be

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