下载文档原格式
Chapter 24 Diffraction
When monochromatic light from a distance source (or a laser) passes through a narrow slit and is then intercepted by a viewing screen, the light produces on the screen a diffraction pattern like that in figure.
This pattern consists of a
broad and intense (very
bright) central maximum and a number of narrower and less intense maxima (called secondary or side maxima) to both sides. In between the maxima are minima.
24.1 Diffraction by a Single Slit
1.Let us consider how plane
waves of light of
wavelength are
diffracted by a single long
narrow slit of width a in an
otherwise opaque screen B,
as shown in cross section in
figure (a).
2.We can justify the central
bright fringe seen in figure
by noting that the waves from all points in the slit travel about the same distance to reach the center of the pattern and thus are in phase there. As for the other bright fringes, we can say only that they are approximately halfway between adjacent dark fringes.
3. To locate the first dark fringe at point P 1, we first mentally divide the slit into two zones of equal widths 2/a . Then we extend to P 1 a light ray r 1 from the top point of the top zone
and a light ray r 2 from
the top point of the
bottom zone . A central
axis is drawn from the
center of the slit to
screen C, and P 1 is
located at an angle θ to
that axis. The first dark
fringe can be located at
2
sin 2λθ=a . It means
λθ=sin a . 4. To find the second dark
fringes above and below
the central axis, we
divide the slit into four zones of equal widths 4/a , as shown in above figure (a). We then extend rays r 1, r 2, r 3, and r 4 from the top points of the zones to point P 2, the location of the second dark fringe above the central axis. The second dark fringe can then be located at 2sin 4λθ=a or λθ2sin =a .
5. The dark fringes can be located with the following general equation : ,3,2,1sin ==m for m a λθ. Above equation is derived for the case of a D >>. However, it also apply if we place a converging lens between the slit and the viewing screen and
then move the screen
in so that it coincides
with the focal plane of
the lens .
6. Intensity in single-slit
diffraction : We can
prove the expression
for the intensity I of
the
pattern as
2)sin (ααm I I =, where
θλπαsin a =, and m I is
the greatest value of
the intensity in the
