An investigator finds a fiber at a crime scene that he wishes to use as evidence
ID: 1321797 • Letter: A
Question
An investigator finds a fiber at a crime scene that he wishes to use as evidence against a suspect. He gives the fiber to a technician to test the properties of the fiber. To measure the diameter of the fiber, the technician places it between two flat glass plates at their ends as in the figure below. When the plates, of length 16.0 cm, are illuminated from above with light of wavelength 630 nm, she observes bright interference bands separated by 0.585 mm. What is the diameter of the fiber?
_________________ ?m
Explanation / Answer
If you're in PY212 at NCSU, the solution to essentially the same problem is in the Serway textbook on pg 834.
The interference pattern is created by the thin film of air having variable thickness. The pattern is a series of alternating bright and dark parallel bands. A dark band corresponds to destructive interference, and there is one phase reversal, so 2*n*t=m*lambda should be used. We can also use similar triangles to obtain the relation t/x = D/L. We can find the thickness for any m, and if the position x can also be found, this last equation gives the diameter of the hair, D.
Solve the destructive interference equation for the thickness of the film, t, with n=1 for air:
t=m*lambda/2
If d is the distance from one dark band to the next, then the x-coordinate of the mth band is a multiple of d:
x=m*d
We are given that d=0.585mm. Now using similar triangles, substitute all the information:
t/x = lambda/(2*d) = D/L ---> D = lambda*L/(2*d)
For your particular problem, this works out to:
630nm*16cm/(2*.585mm) = 86.0 um = 8.6x10^-5 m
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