A soap bubble (n=1.33) is floating in air. If the thickness of the bubble wall is 115nm, what is the wavelength of the light that is most strongly reflected
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Answer:
With phase reversal in the reflection at the outer surface of the soap film and no reversal on reflection from the inner surface, the condition for constructive interference in the light reflected from the soap bubble is
2t=(m+
2
1
)λ
n
=(m+
2
1
)
n
λ
→2nt=(m+
2
1
)λ
λ=
(m+
2
1
)
2nt
where m=0,1,2,.... For the lowest order reflection (m=0), and the wavelength is
λ=
(0+1/20
2nt
=
1/2
2(1.33)(120nm)
=638nm
(b) A thicker film would require a higher order of reflection, so use a larger value of m.
(c) From (a) above, for a given wavelength, the thickness would be
t=(m+
2
1
)
2n
λ
=(m+
2
1
)
2(1.33)
638nm
The next greater thickness of soap film that can strongly reflect 638 nm light corresponds to m=1, giving
t=(m+
2
1
)
2n
λ
=(1+
2
1
)
2(1.33)
638nm
=360nm
and the third such thickness (corresponding to m=2) is
t=(m+
2
1
)
2n
λ
=(2+
2
1
)
2(1.33)
638nm
=600
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