Optics-Diffraction of Thin Hair

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In summary, the problem involves using the diffraction equation to find the thickness of a human hair illuminated with a laser. The distance from the center to the first minimum is given as 4.8 mm and the wavelength of the laser is 748 nm. By plugging these values into the equation and setting m=1, the calculated thickness of the hair is approximately 0.296 mm. However, upon further examination, the correct distance from the screen is 1.09 m, resulting in a thickness of around 0.17 mm. This is in line with the expected thickness of a human hair.
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sheri1987
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Optics--Diffraction of Thin Hair

Homework Statement



A human hair is illuminated with a laser and it produces a diffraction pattern on a screen 1.09 m away. If the distance from the center to the first minimum is 4.8 mm and the wavelength of the laser is 748 nm, what is the thickness of the hair? Express your answer in mm.


Homework Equations



wavelength = (x/m)*(w/l)

x= distance from central maximum to position of the minimum m
l= distance
w= width
m = minimum

The Attempt at a Solution



I converted 748nm to mm and 1.9m to mm and plugged in the values into the above equation and got .296 mm approximately. I set m = 1, because I thought it was asking for the 1st minimum. And x = 4.8...but the answer I got is wrong. Any help?
 
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  • #2


I didn't go through your question, but I would have used the diffraction equation:

[tex]d\sin\theta=m\lambda[/tex]

You can treat an opaque body as a "slit". See Babinet's Principle
 
  • #3


In the problem you say 1.09 m and then you use 1.9 m.
With 1.09 m you get around 170 microns (or 0.17 mm) which is OK for the thickness of hair.
 
  • #4


Thank you very much!
 

1. How does diffraction of thin hair occur?

Diffraction of thin hair occurs when light waves encounter the fine strands of hair. As the light waves pass through the hair, they are scattered and diffracted in various directions, resulting in a halo or a fuzziness around the hair.

2. What factors affect the diffraction of thin hair?

The diffraction of thin hair is affected by the thickness and density of the hair, as well as the angle at which the light is hitting the hair. The wavelength of the light and the distance between the hair and the light source also play a role in the diffraction pattern.

3. Can diffraction of thin hair be observed with the naked eye?

Yes, the diffraction of thin hair can be observed with the naked eye, especially in certain lighting conditions. However, it may be easier to observe with the help of a magnifying glass or a microscope.

4. What are the practical applications of studying diffraction of thin hair?

Studying the diffraction of thin hair has various practical applications in fields such as optics, biology, and forensics. It can help in understanding the structure and properties of hair, as well as in identifying individuals through hair analysis.

5. How can diffraction of thin hair be minimized or prevented?

To minimize or prevent the diffraction of thin hair, one can use anti-frizz products or comb the hair to align the strands. Additionally, using a light source with a shorter wavelength or adjusting the angle of the light can also reduce the diffraction effect.

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