Answer:
The minimum thickness of the film and the wavelength of the light in air are [tex]1.197\times10^{-7}\ m[/tex] and 371 nm.
Explanation:
Given that,
Refractive index of soap= 1.34
Refractive index of glass= 1.55
Wavelength = 642 nm
(I). We need to calculate the minimum thickness
Using formula of thickness
[tex]t=\dfrac{(2m+1)\lambda}{4n}[/tex]
Where, m = 0 for constrictive
Put the value into the formula
[tex]t=\dfrac{(642\times10^{-9})}{4\times1.34}[/tex]
[tex]t=1.197\times10^{-7}\ m[/tex]
(II). We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda=\dfrac{2nt}{m}[/tex]
Where, m = 1
Put the value into the formula
[tex]\lambda=\dfrac{2\times1.55\times1.197\times10^{-7}}{1}[/tex]
[tex]\lambda=371\ nm[/tex]
Hence, The minimum thickness of the film and the wavelength of the light in air are [tex]1.197\times10^{-7}\ m[/tex] and 371 nm.
