How Does Covering One Slit Affect the Double Slit Experiment's Fringe Intensity?

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Covering one slit in the Double Slit Experiment alters the intensity of the fringe pattern observed on the screen. When one slit is covered with a filter that reduces its amplitude by half, the resulting intensity pattern changes, leading to a decrease in overall fringe visibility. The intensity at any point on the screen can be expressed in terms of the original intensity I_{o}, reflecting the impact of the reduced amplitude. The fringe width increases as the distance from the slits to the screen decreases, but the intensity does not remain constant; it varies based on the contributions from both slits. Understanding these changes is crucial for analyzing interference patterns in wave optics.
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1. In a typical set up of Young's Double Slit experiment, if the widths of the slits are assumed to be infinitely small and 'y' is the distance from the central maxima on the screen, sketch a clearly labelled graph to show the variation of the intensity of the fringe pattern with 'y'. The intensity of the waves from each slit is I_{o}. Express the intensity in terms of I_{o}.

My thoughts: The fringe width increases when the distance of the slits from the screen decreases. But doesn't the intensity remain constant??

2. If one of the slits is now covered with a filter such that the light emerging from it is reduced in half the amplitude, sketch on the same graph for the previous question, the new intensity pattern you would expect to observe.

Please help me with the questions.
 
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