# Optics-Diffraction of Thin Hair

1. ### sheri1987

48
Optics--Diffraction of Thin Hair

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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

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

3. 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?

2. ### phyzmatix

362
Re: Optics--Diffraction of Thin Hair

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

$$d\sin\theta=m\lambda$$

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

3. ### nasu

Re: Optics--Diffraction of Thin Hair

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. ### sheri1987

48
Re: Optics--Diffraction of Thin Hair

Thank you very much!