Optics Question 872
Question: A physics professor wants to find the diameter of a human hair by placing it between two flat glass plates, illuminating the plates with light of vacuum wavelength $ \lambda =552nm $ and counting the number of bright fringes produced along the plates. The Professor find 125 bright fringes between the edge of the plates and the hair. What is the diameter of the hair?
Options:
A) $ 525\times {{10}^{-9}}m $
B) $ 344\times {{10}^{-3}}m $
C) $ 3.44\times {{10}^{-5}}m $
D) None of the above
Show Answer
Answer:
Correct Answer: C
Solution:
[c] The reflections from the boundaries will cause a net $ 180{}^\circ $ phase shift.
The condition for bright fringes is
$ 2t=(m+{\scriptstyle{}^{1}/{} _{2}}){\lambda _{film}} $
Now, m=124 since there is a bright fringe for m = 0 and
$ {\lambda _{film}}=\frac{\lambda }{n} $
$ t=\frac{( m+\frac{1}{2} ){\lambda _{film}}}{2}=\frac{( m+\frac{1}{2} )\lambda }{2n} $
$ =\frac{( 124+\frac{1}{2} )(552\times {{10}^{-9}}m)}{2\times (1.00)}=3.44\times {{10}^{-5}}m $
