An unknown liquid is spilled onto a glass table, creating a maximum of reflection with blue light that has a wavelength of 455 nm. Suppose the maximum occurs in the first order, determine the thickness of the liquid (n=1.26).
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To determine the thickness of the liquid, we need to use the equation for constructive interference in thin films, known as the film thickness equation:
2nt = mλ
Where:
- n is the refractive index of the liquid (given as 1.26).
- t is the thickness of the liquid film.
- m is the order of the interference (given as 1 for first order).
- λ is the wavelength of the light (given as 455 nm).
Now, let's solve for t:
2nt = mλ
Substituting the known values:
2 * 1.26 * t = 1 * 455 nm
2.52t = 455 nm
To solve for t, we divide both sides of the equation by 2.52:
t = 455 nm / 2.52
t ≈ 180.56 nm
Therefore, the approximate thickness of the liquid film is 180.56 nm.