Diffraction and Interference of Waves
(SPH 4U1)
Diffraction: the __________________ and ______________________ of a wave
whose wavelength is comparable to or _________________ than the slit width, _____.
Example:
The amount of diffraction can be controlled by the ________________ and the slit
width. A shorter wavelength will diffract ______________.
Constructive interference: when the crest of one wave meets the _____________ of
another wave, the result is a _______________ amplitude
Destructive interference: when the crest of one wave meets the _______________ of
another wave, the result is a _______________ amplitude
A pair of identical point sources that are ___ _____________ will produce a symmetrical
pattern of ___________________ interference areas and ______________ lines.
Example:
Thick lines represent crests and
thin lines represent troughs.
When two crests or two troughs
interfere, the amplitude
_______________. When a
trough from one source meets a
crest from the other, the
amplitude _____________
creating a _____________ line.
Mathematics of Two Point Source Interference
The key to understanding the mathematics of the pattern is looking at the ___________
length from each source, S1 and S2 to the interested point which is either at a location of
constructive interference or at a nodal line.
When the difference in path length is a __________________ multiple of λ,
constructive interference is occurring
When the difference in path length is a ___________ multiple of λ, destructive
interference is occurring and it must be a nodal line
Results:
1
|𝑃𝑛 𝑆1 − 𝑃𝑛 𝑆2 | = (𝑛 − )λ
2
1 λ
sin 𝜃𝑛 = (𝑛 − )
2 𝑑
Where Pn is any point on the nth nodal line
Where 𝜃𝑛 is the angle for the nth nodal line and d is the distance
between the point sources
sin 𝜃𝑛 =
𝑥𝑛
𝐿
Where 𝑥𝑛 is the perpendicular distance from the right bisector
to the point Pn and L is the distance from Pn to the midpoint of
the two sources
𝑥𝑚 =
𝑚𝐿λ
𝑑
Where 𝑥𝑚 is the perpendicular distance from the right bisector
to the point Pm on the mth line of constructive interference
Practice Questions:
1. Two sources are 10.0 cm apart. An interference pattern is observed at a distance of
25.0cm along the right bisector of the line segment joining the sources. The third nodal
line is 33.6 cm from the right bisector at this distance. What is the wavelength of the
waves?
2. Two identical point sources are 5.0cm apart, in phase and vibrating with a frequency of
12 Hz. They produce an interference pattern. A point on the first nodal line is 5cm from
one source and 5.5 cm from the other. Determine the wavelength and speed of the waves.