A surprising result of wave theory is that the diffraction pattern of a dark screen with a hole cut in it (of arbitrary shape) is identical to the pattern of an object with the same shape as the hole.

An application of this principle is that a line mounted on transparent slide casts the same diffraction pattern as a dark film with a slot of equal size cut in it. This principle is used to measure the width of a hair. If the distance between the first spot and the central minimum is s = 1.6 cm, L = 8 m, and λ = 3 x 10^–7 m, what is the width of the hair?

So, I'm trying to apply this formula: s/L = λ/d --> and I am looking for d.
So rearranged, the formula would be d = λL/s
I convert all the units properly and then the answer I get is d = 0.15 millimeters.

Am I doing it right or am I not even using the right formula. I'm a little confused by what "s = the distance between the first spot and the central minimum" means. Please help!

1 answer

  1. That is the formula, almost,but for small angles, it is ok to use.
    The width of a human hair is .15mm for a black person. For caucasians, it is about half that.

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