Explanation:
It is given that,
The thinnest soap film appears black when illuminated with light with a wavelength of 535 nm, [tex]\lambda=5.35\times 10^{-7}\ m[/tex]
Refractive index, [tex]\mu=1.33[/tex]
We need to find the thickness of soap film. The soap film appear black means there is an destructive interference. The condition for destructive interference is given by :
[tex]2t=m\dfrac{\lambda}{\mu}[/tex]
t = thickness of film
m = 0,1,2....
[tex]\mu[/tex] = refractive index
[tex]t=m\dfrac{\lambda}{2\mu}[/tex]
[tex]t=\dfrac{\lambda}{2\mu}[/tex]
For thinnest thickness, m = 1
[tex]t=1\times \dfrac{5.35\times 10^{-7}\ m}{2\times 1.33}[/tex]
[tex]t=2.01\times 10^{-7}\ m[/tex]
Hence, this is the required solution.
