$($a$)$ A periodic transparency described by $4$fx$=4$;x$\_(0)=5($x$)/($x$\_(0))$t$($x$,$y$)=\backslash$sum$\_(-\backslash$infty $)^(\backslash$infty $)$ rect$(($x$-$mx$\_(0))/($x$)),$x is placed at the

object plane of a $4$f system and a small opaque stop is placed on the common focal plane.

$($i$)$ Draw the setup and sketch the transparency function with x$=4$;x$\_(0)=5.[2]$

$($ii$)$ Sketch the $($i$)$ optical field, $($ii$)$ intensity distributions at the image plane. Give reasons for

your answer. $[1+2].$

$($iii$)$ What is the range of$($ x$)/($x$\_(0))$ for which one would get contrast reversal? Give reasons for your

answer. $[1]$