Question

A certain region of a soap bubble reflects red light of wavelength $\lambda =650nm$. What is the minimum thickness that this region of the soap bubble could have? Take the index of the refraction 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

The correct option is A $1.2\times {10}^{-7}m$

There is air on both sides of the soap film. Therefore, the reflections of the light produces a net ${180}^{\circ }$ phase shift.
The condition for bright fringes is
$2t=(m+\frac{1}{2}){\lambda }_{film}$
$t=\frac{(m+\frac{1}{2}){\lambda }_{film}}{2}=\frac{(m+\frac{1}{2})\lambda }{2n}$
$=\frac{\left(\frac{1}{2}\right)(650\times {10}^{-9}m)}{2\left(1.41\right)}1.2\times {10}^{-7}m$