Question

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.

Answer 1

Ray 1 has a longer path than that of ray 2 by a distance `d sin 45^(@)`, before reaching the slits. Afterward 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^(@)`
a. central maximum is obtained where net path difference is zero `theta = 45^(@)`
b. Third order maxima is obtained where net path difference is `3 lambda`, or
`d sin theta = d sin 45^(@) = 3 lambda`
`sin theta = sin 45^(@) + (3 lambda)/(d)`
putting `d = 20 lambda`, we have
`sin theta = sin 45^(@) + (3 lambda)/(12 lambda)`
or `theta = sin^(-1) [(1)/(sqrt 2) + (3)/(20)]`.