Optics-Diffraction of Thin Hair

[sheri1987]

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?

 

[phyzmatix]

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

 

[nasu]

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.

 

[sheri1987]

Thank you very much!