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Unformatted text preview: Wave Optics 24.22 315 Light reflecting from the lower surface of the air layer experiences phase reversal, but
light reflecting from the upper surface of the layer does not. The requirement for a dark
fringe (destructive interference) is then
λ
2 t = mλn = m = m λ , where m = 0 , 1, 2,… nair At the thickest part of the film ( t = 2.00 µ m ) , the order number is
m= 2t λ = 2 ( 2 .00 × 10 −6 m )
546.1 × 10 −9 m = 7.32 Since m must be an integer, m = 7 is the order of the last dark fringe seen. Counting the
m = 0 order along the edge of contact, a total of 8 dark fringes will be seen. 24.23 With a phase reversal upon reflection from the
lower surface of the air layer and no phase change
for reflection at the upper surface of the layer, the
condition for destructive interference is
λ
2 t = mλn = m = m λ , where m = 0 , 1, 2,… nair Counting the zeroth order along the edge of
contact, the order number of the thirtieth dark
fringe observed is m = 29 . The thickness of the air
layer at this point is t = 2r , where r is the radius of
the wire. Thus,
−9
t 29 λ 29 ( 600 × 10 m )
=
= 4.35 µ m
r= =
2
4
4 Incident
light
n
t3 t2
t1
O ...
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This document was uploaded on 10/20/2011.
 Spring '09
 Physics, Work, Light

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