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A thin film of soap with [tex]n = 1.37[/tex] hanging in the air reflects dominantly red light with [tex]\lambda = 696 \, \text{nm}[/tex]. What is the minimum thickness of the film?

Answer :

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]

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