Distance between the slit shown in figure is `d = 20 lambda`, where `lambda` is the wavelength of light used. Find the angle `theta` where
a. central maxima (where path difference is zero) is obtained, and
b. third-order maxima is obtained.

Explanation

Ray 1 has a longer path than that of ray 2 by a distance d `sin 45^(@)` before reaching the slits. Afterwords ray 2 has a path longer than ray 1 by a distance `d sin theta` The net path difference is therefore, `d sin theta -d sin 45^(@)`
(i) Central maximum is obtained, where not path difference is zero or
`d sin theta-d sin 45^(@) =0 or theta=45^(@)`
(ii) Third order maxima is obtained, where net path difference is `3lambda`
or `d sin theta -d sin 45^(@)=3lambda`
`:. sin theta = sin 45^(@)+(3lambda)/d`
Putting `d=20 lambda`
we have `sin theta=sin 45^(@)+(3lambda)/(20 lambda) or theta ~~59^(@)`