Question
A certain region of a soap bubble reflects red light of wavelength $$\lambda = 650\,nm.$$ What is the minimum thickness that this region of the soap bubble could have? Take the index of reflection of the soap film to be $$1.41.$$
A.
$$1.2 \times {10^{ - 7}}m$$
B.
$$650 \times {10^{ - 9}}m$$
C.
$$120 \times {10^{ 7}}m$$
D.
$$650 \times {10^{ 5}}m$$
Answer :
$$1.2 \times {10^{ - 7}}m$$
Solution :
There is air on both sides of the soap film.
∴ the reflections of the light produce a net $${180^ \circ }$$ phase shift.
The condition for bright fringes is $$2t = \left( {m + \frac{1}{2}} \right){\lambda _{{\text{film}}}}$$
$$\eqalign{
& t = \frac{{\left( {m + \frac{1}{2}} \right){\lambda _{{\text{film}}}}}}{2} = \frac{{\left( {m + \frac{1}{2}} \right)\lambda }}{{2n}} \cr
& = \frac{{\left( {\frac{1}{2}} \right)\left( {650 \times {{10}^{ - 9}}m} \right)}}{{2\left( {1.41} \right)}} \cr
& = 1.2 \times {10^{ - 7}}\,m \cr} $$