91Ó°ÊÓ

(a) Destructive interference (dark fringes) occurring at an angle

As the sine values bounded between -1 and 1, therefore m is bounded by;

Hence, this means there are 39 completely dark fringes on both sides of the central maximum, for a total of 78 completely dark fringes.

(b) For a maximum integer (m) smaller than $a/\mathrm{λ}$, the dark fringe that is farthest from the central maximum appears;

Hence, the angle is$80.8°$

(c) The pattern begins with a dark fringe and ends with a light fringe. As a result, the 38^th light fringe is the light fringe that comes before the 39^th dark fringe. for large m, the maximum intensity of the mth light fringe, the equation is;

The most distant 39^th dark fringe occurs at an angle${\mathrm{θ}}_{d39}={\mathrm{θ}}_{dmax\text{'}}$ , therefore the 38^th dark fringe is expressed by the equation;

The midpoint between the angles of these two dark fringes is where the 38th light fringe reaches its maximum intensity.