IB Physics SL IA (Internal Assessment): The relationship between the width of a hair strand and its diffracted pattern in determining the wavelength of a laser light.
Received level 6 by IB exam board.
IB Physics Internal Assessment
The relationship between the width of a hair strand and its diffracted pattern in
determining the wavelength of a laser light
Introduction
My interest in diffraction sparked at a young age when my brother and I would play with lasers and point them at
several objects within our home. We were often left astounded by the unusual patterns created by the light. Being
young, however, the concept was difficult for me to grasp. As I grew older and understood
the world of physics in more depth (both in out and out of school), I started understanding
the idea and the theory behind it. Furthermore, being from the island of Cyprus and
spending much of my time there, I often came across the real-life observation of
diffraction by observing the water waves in the ocean. In fact, this summer whilst I was
there, I came across an article published by ScienceNewsforStudents ("Measure The
Width Of Your Hair With A Laser Pointer") which explained a weird phenomenon: one
being that a hair strand creates a diffracted pattern when being pointed at directly with a
laser light. This helped grow my curiosity on diffraction as a topic of interest even further.
After replicating the experiment, I wanted to investigate whether I could reverse the
dependent and independent variables: using different widths of hair to determine the Figure 1: Diffraction produced by
wavelength of a laser light. boat in Cyprus
Research question
How can the wavelength of a laser light, diffracted through a hair strand, be determined by the relationship between
a hair strand’s width and the distance between the centre and the first diffraction minimum?
Background information
According to the laws of physics, light waves tend to bend around obstacles and openings, spreading out as a result
of the light waves passing through a slit, which is relative or smaller than the light’s wavelength and the amplitudes
of the waves. In the case of this investigation, diffraction around a thin object is expected to behave in the same
way as diffraction through a single-slit. In general, and in specific to this experiment, single-slit diffraction occurs
when the laser light is incident upon the object (the hair strand) and diffracts around it, creating dark and light
fringe patterns. This experiment is a variation of single-slit diffraction, as the light wave bends around the edges of
the hair strand. Huygens’s principle is used in explaining this phenomenon.
Huygens’s principle states that each wavefront can be treated as an envelope
of component wavelets and thus, each point on a wavefront can be seen as a
spherical wavelet, acting as an independent source in generating wavelets
1
Figure 2: Huygens’s principle- the
phenomena of light spreading, creating a
diffraction pattern
, from that point. The spherical wavelets pass and interfere with one another when travelling through slits, thus
creating a pattern on a wall; which partly absorbs the light. Subsequently, the wavelets create a central maximum as
they move forward (figure 2, right). The diffracted patterns on the wall each employ a dissimilar distance to each
slit. The above is demonstrated by figure 2, left, where one can see a schematic demonstrating Huygens’s principle,
in particular, the superposition of wavelets.
The wavelength of a laser light can be determined via the pattern of diffraction (formed by dark and light fringes).
In the 1800s, French physicist Jacques Babinet documented ‘Babinet's Principle’: the diffraction arises from
Huygens-Fresnel principle, wherein the diffraction stems from the mutual interference of the secondary wavelets
originating from the wave-front. The principle suggests that there is a duality between objects and openings
whereby the spacing of the interference pattern from the hair is the same spacing we would expect for a narrow
opening of the same width. As this technique aims to measure small objects, it can be used in measuring small
openings.
In this investigation, the laser light interferes, by passing directly through the
middle of the hair (as depicted in figure 3) because when parallel waves of
light are obstructed by very small objects (i.e. a sharp edge, slit, wire, etc.),
the waves spread around the edges of the obstruction and interfere, resulting
in a pattern of dark and light fringes. It is important to note that the hair strand
has the same width throughout its length. The pattern of dark and light
fringes represents the phenomena of constructive and destructive interference,
Figure 3: Set-up before experiment shown in Figure 4. Constructive interference (Figure 4, left) occurs when two
“Laser
wavesinterference”
are in phase and overlap thereby causing the displacement to be the sum of both amplitudes and light
intensity to add, creating the red and bright fringe. On the other hand, destructive interference (Figure 4, right) is
produced when 2 waves are displaced in the opposite
direction, causing the displacement to be the result of the
difference between the two amplitudes, creating the dark
fringe. As the laser light shines through the hair strand, the
light diffracts. Moreover, as light travels toward the wall, it
travels at various intervals, where the light waves add or
Figure 4: The interference of two waves. Constructive
cancel each other, creating a pattern. interference (left), destructive interference (right)
In order to focus even more on this experiment and its aim, we will restrict ourselves to Fraunhofer’s diffraction.
This special case of diffraction suggests that the light rays that are diffracted are roughly parallel to one another.
This is because the width of the slits and obstacles are small and finite, in which Fraunhofer’s experiment arises. In
order to simplify the experiment, every point of the wave can be matched with another which finds itself to be at a
a λ
distance away and is out of phase with a path difference of . Thus, the first minimum follows the following
2 2
a λ
condition: sin θ=
2 2
¿ θ follows small angle approximation ( as θ is small−less than 10 ° )∗¿
Thus, α sinθ=λ
αθ= λ
2
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