Optics Question 875
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 reflection of the soap film to be 1.41.
Options:
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 $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] There is air on both sides of the soap film.
$ \therefore $ the reflections of the light produce a net $ 180{}^\circ $ phase shift.
The condition for bright fringes is $ 2t=(m+{\scriptstyle{}^{1}/{} _{2}}){\lambda _{film}} $
$ t=\frac{(m+{\scriptstyle{}^{1}/{} _{2}}){\lambda _{film}}}{2}=\frac{(m+{\scriptstyle{}^{1}/{} _{2}})\lambda }{2n} $
$ =\frac{({\scriptstyle{}^{1}/{} _{2}})(650\times {{10}^{-9}}m)}{2(1.41)}=1.2\times {{10}^{-7}}m $
