Single Slit Diffraction
In the previous chapter we calculated the interference pattern
from a pair of slits.
One of the assumptions in
the calculation was that
the slit width was very
small compared with the
wavelength of the light.
a

Now we consider the
effect of finite slit
width. We start with a
single slit.
Each part of the slit acts as a source of light waves, and
these different light waves interfere.





Divide the slit in half.
Ray  travels farther*
than ray  by (a/2)sin.
Likewise for rays  and
.
a/2
a/2
If this path difference is exactly half a
wavelength (corresponding to a
phase difference of 180°) then the
two waves will cancel each other and
destructive interference results.
Destructive interference:

a





a
sin 
2
a

sin =
2
2
*All rays from the slit are converging at a point P very far to the right and out of the picture.
Destructive
interference:
a

sin =
2
2
a sin = 

sin =
a
a/2

a
a/2
a
sin 
2
If you divide the slit into 4 equal parts, destructive
2
interference occurs when sin = .
a
If you divide the slit into 6 equal parts, destructive
3
interference occurs when sin = .
a





a/2

a
a/2
a
sin 
2
In general, destructive interference occurs when
a sin = m, m =1, 2, 3, ...
The above equation gives the positions of the dark fringes.
The bright fringes are approximately halfway in between.
Applet.





a sin =m
http://www.walter-fendt.de/ph14e/singleslit.htm
Use this geometry for
tomorrow’s single-slit
homework problems.
y
a
If  is small,* then it is
valid to use the
approximation sin   .
( must be expressed in
radians.)

O
x
*The approximation is quite good for angles of 10
or less, and not bad for even larger angles.
Single Slit Diffraction Intensity
Your text gives the intensity distribution for the single slit.
The general features of that distribution are shown below.
Most of the intensity is in the central maximum. It is twice
the width of the other (secondary) maxima.
Starting equations for single-slit intensity:
2
=
a sin

 sin  /2  
I = I0 


/2
 
 
“Toy”
2