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Interference/Double Slit

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 [tex] I_{o} [/tex]. Express the intensity in terms of [tex] I_{o} [/tex].

My thoughts: The fringe width increases when the distance of the slits from the screen decreases. But doesnt 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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