Quantitative Investigation of the Texture of a Hair Strand Using Single-Slit Diffraction

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  • Topic: Hair, Diffraction, Laser
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  • Published : January 27, 2013
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Quantitative Investigation of the Texture of a Hair Strand

using Single-Slit Diffraction

Stephen Flores1, Ailene Gonzales2
Department of Physics, University of San Carlos, Nasipit, Talamban, Cebu City 6000 1step.upflores@yahoo.com
2avg08_1s2 @yahoo.com
Abstract
This paper presents the utilization of the single slit-diffraction phenomena in analyzing the physical characteristics of a hair strand. Hair samples with various macroscopic textures were used as barriers to produce a diffraction pattern where the distance between fringes were readily obtained using a program that displays its line profile. The eccentricity values, [pic], are (0.12±0.01), (0.29±0.04), (0.33±0.01), (0.35±0.03) for Sample 1 to 4 respectively. Almost all of the samples exhibit eccentricities of less than 0.5 which means all of them are fairly straight. But in comparison, the eccentricities show that Samples 1 is a fairly straight hair while Samples 2, 3 and 4 are wavy hairs. These implications conform to the real macroscopic texture of each hair strand.

1. Introduction
Hair strands, such as those of the animals and humans have been of particular interests in different fields since it offers variety of information. In forensic investigation for instance, a strand of hair is considered important evidence in pointing out the identity of whoever was in the crime scene. In fields such as this, the biological attributes of the human hair is analyzed for DNA identification. In this experiment, the physical characteristic of the human hair is quantitatively investigated using one of physics’ useful phenomena known as diffraction. This occurs when a wave such as light passes around an obstacle or through an opening. Aside from this study, diffraction has also been cleverly taken advantage of in applications such as x-ray diffraction of crystals and holography [1].

2. Theory
According to Babinet’s principle, the diffraction pattern produced by a barrier is identical to that produced by the opening complementary to the barrier. The principle of Babinet is a useful tool which provides flexibility in the solution of aperture diffraction problems in optics and electromagnetic. This principle was proposed by Babinet in 1837 & states that the sum of the scattered fields by an obstacle & its complementary aperture leads to an unobstructed incident wave [3].

[pic]

Figure 1. The opaque plate with star-shaped holes on the left is complementary to the plate on the right that consists of opaque stars. If both are illuminated with light of the same wavelength, identical diffraction patterns are produced [4].

Fig. 2 shows diffraction by a single slit; monochromatic light sent through a narrow slit of width a produces a diffraction pattern on a distant screen. Equation 1 gives the condition for the destructive interference (a dark fringe) at a point in the pattern at angle θ. [pic] (1) The plus-or-minus sign in Eq. 1 says that there are symmetrical dark fringes above & below point O in Fig.1. The values of θ are often so small that it can be approximated as sin θ = θ (where θ is in radians). Equation 1 can be written as [pic] (2) If the distance from slit to screen is x and the vertical distance of the mth dark band from the center of the pattern is Ym, then [pic] = [pic] . For small θ, [pic], and then we find Eq. 3[1]. [pic] (3) Rearranging Equation [3] to solve for hair diameter, a,

[pic] (4)
In performing the hair...
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