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 $$\lambda = 552\,nm$$ 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?
A.
$$525 \times {10^{ - 9}}\,m$$
B.
$$344 \times {10^{ - 3}}\,m$$
C.
$$3.44 \times {10^{ - 5}}\,m$$
D.
None of above
Answer :
$$3.44 \times {10^{ - 5}}\,m$$
Solution :
The reflections from the boundaries will cause a net $${180^ \circ }$$ phase shift.
The condition for bright fringes is $$2t = \left( {m + \frac{1}{2}} \right){\lambda _{{\text{film}}}}$$
Now, $$m= 124$$ since there is a bright fringe for $$m=0$$ and $${\lambda _{{\text{film}}}} = \frac{\lambda }{n}$$
$$\eqalign{
& t = \frac{{\left( {m + \frac{1}{2}} \right){\lambda _{{\text{film}}}}}}{2} = \frac{{\left( {m + \frac{1}{2}} \right)\lambda }}{{2n}} \cr
& = \frac{{\left( {124 + \frac{1}{2}} \right)\left( {552 \times {{10}^{ - 9}}\,m} \right)}}{{2 \times \left( {1.00} \right)}} \cr
& = 3.44 \times {10^{ - 5}}\,m \cr} $$