Answer:
The thickness is [tex]t = 1.273 *10^{-7} \ m[/tex]
Explanation:
From the question we are told that
The refractive index of the film is [tex]n = 1.37[/tex]
The wavelength is [tex]\lambda = 696 \ nm = 696 *10^{-9 } \ m[/tex]
Generally the condition for constructive interference in a film is mathematically represented as
[tex]2 * t = [m + \frac{1}{2} ] \lambda_k[/tex]
Here t is the thickness of the film , m is the order number (0, 1, 2, 3 ... )
[tex]\lambda _k[/tex] is the wavelength of light that is inside the film , this is mathematically evaluated as
[tex]\lambda _k = \frac{ \lambda }{ n}[/tex]
[tex]\lambda _k = \frac{ 696 *10^{-9}}{ 1.37}[/tex]
[tex]\lambda _k = 5.095 *10^{-7 } \ m[/tex]
So for m = 0
[tex]t = [ 0 + \frac{1}{2} ] \lambda _k * \frac{1}{2}[/tex]
substituting values
[tex]t = [ 0 + \frac{1}{2} ] (5.095 *10^{-7}) * \frac{1}{2}[/tex]
[tex]t = 1.273 *10^{-7} \ m[/tex]
