Looking straight downward into a rain puddle whose surface is covered with a thi

Question

Looking straight downward into a rain puddle whose surface is covered with a thin film of gasoline, you notice a swirling pattern of colors. The point directly beneath you is colored a beautiful iridescent green. You happen to remember that the index of refraction of gasoline is 1.38 and that the wavelength of green light is 540 nm. (a) What is the minimum possible thickness of the gasoline layer directly beneath you? (b) The surface of the puddle shifts and now the point below you is now violet, and you recall violet has a wavelength of roughly 400 nm. By how much did the thickness of the gasoline layer change?

Explanation / Answer

Here in the given problem, we will use the formula for the reflection of light for a thin film,

(m - 0.5) = 2 x n x d x cos()

(where m = maxima (1 in given case), n = index of refraction of the film, d = thickness of the film, = angle that the

light is at inside the film)

So, m = 1, n = 1.38, = 0 and = 540 x 10-9 m

(1 - 0.5) x 540 x 10-9 = 2 x 1.38 x d x cos0°

d = 9.78 x 10-8 m = 97.8 nm

b) here, = 400 x 10-9 m

(1 - 0.5) x 400 x 10-9 = 2 x 1.38 x d x cos0°

d = 7.25 x 10-8 = 72.5 nm

Change in thickness, t = 97.8 - 72.5 = 25.3 nm

Please rate my answer if you find it helpful, good luck...

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