INTERFERENCE
Interference is the name given to the effects which occur when two separate
wavetrains overlap. It is interesting that waves usually do not seem to bump
into one other, rather they pass through each other and merge or combine
their effects. For example the different sounds from a group of instruments
played together can be heard combined and merges; the various sound
waves do not collide. The ability of wave motions to combine together is
known as the superposition of waves, and what happens when they
combine is called interference.
Water Waves
Interference is easily demonstrated in a ripple tank. As both vibrators
are producing waves with the same wavelength and are both
simultaneously producing a wave crest or a wave trough. When the
1
1
1
 or 1  or 2  , etc. , destructive
2
2
2
interference occurs, i.e. the regions crests meet troughs. When the path
difference is 0 or 1 or 2 , etc., constructive interference
path difference is
occurs, i.e. the regions crests meet crests or troughs meet troughs.
Fig.a
The point where two waves always cancel out each other and
produce zero displacement is called node (no displacement). The
point where the two waves reinforce each other and produce a
maximum displacement is called an antinode. As shown in Fig.b,
lines of nodes which is known as nodal lines, and lines of antinodes,
termed as antinodal lines can be seen clearly.
Fig.b
Conditions for Wave Interference to be Observable
By interference we mean the superposition of wavetrains from a finite
number of coherent sources. Two sources are frequently used.
The following conditions should be obey in order to make the interference
patterns observable or detectable for all types of wave motion.
(1) The sources must have roughly the same amplitude and exactly
the same frequency.
(2) The sources must be coherent, i.e. they must have a constant
phase relationship.
(3) For polarized waves, the two waves must have the same direction
of polarization .
(4) In the interference of light, monochromatic source is generally
used.
Young's Double-Slit
In Figure c shown on the previous page, light from the monochromatic
(i.e. single frequency) source is diffracted at So so as to illuminate S1
and S2 coherently.
Fig. c
Consider Figure cd. Po is the point directly opposite the midpoint between
S1 and S2. The path difference of the point Po is zero. Therefore
constructive interference occurs at point Po and a bright fringe is observed.
At other places, intensity depends on the path difference. Choose an
arbitrary point P distance x from Po.
path difference
  S2P  S1P
Since
S2P 2  D 2  ( x 
S1P 2  D 2  ( x 
d
2
d
2
)2
)2

S2P2  S1P2  2xd


2xd
S2P  S1P
Since D is set at a distance of 1 m or more and d < 1 mm,

S2P  S1P  D


2xd xd

2D
D
……………………
(1)
WU
W32
(a) Condition for Bright Fringes
If  = n , where n = 0, 1, 2, 3, ….. constructive interference will take
place and intensity is a maximum.
For maximum intensity:
n 
xd
D
i.e. for bright fringes to be observed

x n
D
d
…………………….……… (2)
(b) Condition for Dark Fringes

1
), where n = 0, 1, 2, 3, ….. destructive
2
2
interference will take place and intensity is minimum (zero).
If  = (2n + 1)
= (n +
For minimum intensity:
1
xd
( n  ) 
2
D
i.e. for dark fringes to be observed

1 D
2 d
x  (n  )
……………………… (3)
From (2) and (3) that the fringes are of equal width. Fringe separation, x is
given by
x 
D
d
…………………………..(4)
Although we have derived these equations for light waves, they apply
equally to all types of waves.