Investigating Diffraction Gratings and Double Slit Interference
Diffraction Grating simulates the diffraction of light through a diffraction grating and uses the visual
and graphical display of the diffraction pattern to explore the relationship between slit separation, slit
distance, number of slits, and incident light wavelength.
Prerequisites
Students should be familiar with the properties of waves, including interference patterns, wave phase,
path differences, and destructive and constructive interference patterns. Students should also have a
working knowledge of trigonometry.
Learning Outcomes
This lesson introduces Young's Double Slit Experiment and double slit diffraction. Students will be able
to explain why geometric optics fail to account for the diffraction of light and provide an explanation for
such phenomena by adhering to a wave model of light. Using the applet, students will perform
experiments to investigate the effects of changing wavelength and slit separation on interference
patterns. As well, students will be able to quantitatively solve double slit diffraction grating problems.
Instructions
Students should understand the applet functions that are described in Help and ShowMe. The applet
should be open. The step-by-step instructions on this page are to be done in the applet. You may need
to toggle back and forth between instructions and applet if your screen space is limited.
Procedure
1. Interference Review
This lesson builds upon the concept of wave interference. Interference refers to the way in which two or
more waveforms combine to produce a resultant waveform. There are two different types of
interference: constructive and destructive.
Destructive interference occurs when two waves combine to produce a resultant wave smaller than
either of the original waves. If complete destructive interference occurs, both waves cancel each other
out completely and produce no resultant wave. On an interference pattern this is referred to as a node.
Constructive interference occurs when two waves combine to produce a resultant wave larger than
either of the original waves. If complete constructive interference occurs, both waves combine to
produce the largest possible resultant wave. On an interference pattern this is referred to as an
antinode.
Exercise 1
After viewing the demonstrations in class, draw two waves (one below the other) and the resultant
wave to illustrate:
a. complete constructive interference
b. complete destructive interference
Exercise 2
The diagram below shows two sources that are producing continuous circular waves. Finish the diagram
by drawing 3 more wave fronts so that the interference pattern is visible. Circle each antinode in your
pattern.
2. Young's Double Slit Experiment
Today, most people think of light as being a wave, or at least agree that it has wavelike properties.
Historically, however, there was a long-running, heated debate surrounding the nature of light - was it a
stream of particles, or was it a wave? The physics community was split, but for the most part, the
particle theory of light was accepted.
However, early in the 19th century Thomas Young, a British scientist and doctor, performed an
experiment that provided experimental evidence for the wave model of light. By that time, it was well
known that waves displayed the unique property of diffraction.
Diffraction occurs when a wave front bends or changes direction as it passes by the sharp edge of an
obstacle or through a small opening in the obstacle. As illustrated in Figure 1, waves are diffracted as
they pass through a small opening in a barrier. The amount of diffraction depends on the wavelength
and the size of the opening. A barrier with multiple openings is called a grating.
Young, in his famous "Double-Slit" experiment showed that light could also be diffracted. Young's
experiment was crucial in providing support for the wave model of light.
Exercise 3
Imagine shining light through a grating with two slits. Behind the grating is a screen. If light were a
stream of particles, as stated by the particle model of light, what would you expect to see on the
screen? Complete the diagram.
Exercise 4
On the applet, set the "slit count" to 2. Observe the pattern produced on the screen when light passes
through the two slits. How does this pattern compare to what you predicted in exercise 3? Would you
say that this pattern supports a particle model of light?
Exercise 5
Young's double slit experiment showed that light, when shone through a double slit, was diffracted and
produced a definite interference pattern on a screen. Use the following two questions and the diagram
below to help explain how his experimental results support a wave model of light.
a. Can particles diffract?
b. Can two or more particles constructively or destructively interfere to produce an interference
pattern?
Exercise 6
Young needed to use monochromatic (single color) and coherent light (in phase) for his double slit
experiment. Why were both of these conditions necessary? Hint: use the applet to investigate how the
interference pattern changes when wavelength (color) is varied. Watch what happens to the location of
each bright fringe (antinode) as the color is changed.
Young's experiment helped to convince the scientific community that the behavior of light could be
explained with a wave model. Light displays properties that are unique to waves: interference and
diffraction. In the next section you will explore the phenomena of double slit diffraction more closely.
3. Diffraction, Path Difference, and Interference
Diffraction is the bending, or spreading of a wave front around a sharp corner. For example, when a
wave front approaches a wall with several openings, diffraction occurs and circular wave fronts merge
from the openings. When several wave fronts spread out, interference between the waves will occur.
Path difference can explain interference patterns. If the path difference between wave sources and a
common point is an integral number of waves, then the waves are in phase with one another and
constructively interfere. However, if the path difference is a half number of waves, then the waves
arrive completely out of phase with one another and destructively interfere.
Path difference explains the interference patterns shown in the applet. When light is diffracted,
interference patterns are produced. When the light reaches a screen, bright and dark bands are
observed. These bands are called interference fringes. Bright fringes (antinodal lines) are regions of
constructive interference and dark fringes (nodal lines) are regions of destructive interference. Figure 2
illustrates the fringes and the path differences for the interference pattern created when light is
diffracted through a double slit grating. Notice that the bright and dark fringes are symmetrical around
the central antinode.
Exercise 7
The following diagram shows a wave front approaching a wall with two openings. Finish the diagram by
sketching in the waves after they pass through the openings. On your diagram, label the antinodal and
nodal lines.
Exercise 8
On the applet, while keeping the slit width, slit spacing, and wavelength constant, vary the slit count and
look at the interference fringes on the screen.
a. Why is there always a bright fringe at the centre of the screen (this fringe is called the central
antinode)?
b. Explain why this is always the brightest fringe.
c. Look at the edges of the interference fringes on the screen. Why are the edges not sharp?
4. Double Slit Interference
On the applet, set the slit count to two and explore the characteristics of double slit interference
patterns. Wherever possible, use the applet to help complete the following exercises.
Exercise 9
Complete the table below by observing and describing how different parameters affect the interference
pattern caused by double slit diffraction. You may need to zoom in on the graph to see how the intensity
and theta values (q) change. To zoom in, hold down the control key and drag out an area on the graph.
You can restore the graph by clicking "Restore Graph"
Increase:
Remains constant:
slit width
λ, slit spacing
slit spacing
λ, slit width
λ
slit width, slit spacing
Describe what happens
to the angle of
diffraction (q) between
the central antinode
and the fringes.
Describe what happens
to the number of peaks
beneath the intensity
envelope.
Describe the intensity
of the peaks (the
brightness of the
fringes).
Exercise 10
What happens when the slit width is as wide as possible, but the slit spacing is as small as possible
(compare the intensity graph to the intensity envelope)? Why do you think this happens?
Exercise 11
In the applet, you can shine different colors of light through the double slit. The resulting interference
pattern consists of dark bands and bright bands of the specific color. However, what do think would
happen if you passed white light through the double slit?
a. What color would the central antinode be? Explain.
b. What would the other bright fringes look like? Explain.
The interference pattern produced by diffraction through a double slit can be analyzed using the
following equation.
nλ =dsin⊖
Quantity
Symbol
SI Unit
wavelength
l
m
slit spacing (separation)
d
m
path difference (see below)*
n
none (number of wavelengths)
(q)
degrees
angle of diffraction (measured from the central
antinode)
Constructive interference (antinodes - bright fringes) occurs when the path difference is a whole
number of wavelengths (n = 0, ±1, ±2 ...). Thus, for antinodes or bright fringes: N = 1, 2, 3, 4 ....
* Destructive interference (nodes - dark fringes) occurs when the path difference is offset by half a
wavelength (n = ±0.5, ±1.5, ±2.5 ...). Thus, for nodes or dark fringes: n = 0.5, 1.5, 2.5, 3.5 ....
Exercise 12
Light, with wavelength of 457 nm is shone through two slits that are separated by 0.20 mm.
a. What is the angle of diffraction to the second bright fringe? Show the calculation and check your
answer with the applet. You may need to zoom in on the graph to see accurate theta values (q). To
zoom in, hold down the control key and drag out an area on the graph. You can restore the graph by
clicking "Restore Graph".
b. What is the angle of diffraction to the second dark fringe? Show the calculation and check your
answer with the applet.
Exercise 13
If light is shone through two slits, separated by 0.33 mm, and the first dark fringe is located 0.035° from
the central antinode, what is the wavelength of the light? Show the calculation and check your answer
with the applet.
Exercise 14
Blue light of wavelength 465 nm is incident on a double slit where the slits are spaced 0.5 mm apart and
are 0.05 mm wide. At what angle of diffraction will the fourth order antinodal line appear? Show the
calculation and check your answer with the applet.
Exercise 15
Radiation of 400 nm passes through two slits and produces the following interference pattern. Given the
angle of diffraction for the second order dark fringe, determine the slit separation. Show the calculation
and check your answer with the applet.
5. Summary
In summary, when light is shone through a double slit, it is diffracted and an interference pattern is
created. The interference pattern is described by:

The central antinode or bright fringe that is in the centre of the pattern. On either side of the
central antinode, there is a dark fringe, then a bright fringe, then a dark fringe, then a bright
fringe, etc.

Bright Fringes are the location of constructive interference where the path difference for the
light traveling from both slits is a whole number of wavelengths:

Dark Fringes are the location of destructive interference where the path difference is offset by a
half number of wavelengths:
To explain the interference pattern, the wave model of light was necessary. To this end, Young's double
slit experiment was crucial in establishing the wave nature of light.