We
have to show that the half-width
if
|
Solution: Click For PDF Version We first work out the expression for the intensity of the resultant of two coherent waves with phase difference .
Let the electric field components of the two waves at a point P
at time t be described by the functions
where
W
where the
phase
and the amplitude is
As the intensity I is proportional to the square of the amplitude, we note that
and for small
And
Let the
centre of the m th-
fringe be at angle
Let the
intensity is one-half that at the centre of the fringe at
This implies that
This implies that
The half-width is the angle between the two points in the fringe where the intensity is one-half that at the centre of the fringe. Therefore, half-width of the fringe will be
|
of the double-slit interference fringes is given by
,
is small enough so that
.
The half-width is the angle between the two
points in the fringe where the intensity is one-half that at the
centre of the fringe.
is the angular frequency of the waves and
e
have
is
,
.
.
.
We have
We note that
.
We therefore have
.
