《物理双语教学课件》Chapter 24 Diffraction 衍射理论

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