Respuesta :
Answer:
Looking straight downward into a rain puddle whose surface is covered with a thin film of gasoline, you notice a swirling pattern of colors caused by interference inside the gasoline film. 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 about 540 nm .
Explanation:
In this case we have that the refractive index of gasoline is higher than the refractive index of air and water, therefore the maxima and minima are determined by the relationship:
2 n d = { ( m + 1 /2 ) λ max
m λ min
Since we are observing a colorful pattern, it means that we are observing the interference maximums:
2 n d = ( m + 1/ 2 ) λ ⇒ d = ( m + 1/ 2 ) λ /2 n
∴ ⎪ m = 0 ⇒ d 0 = ( 0 + 1/ 2 ) 538 n m / 2 ⋅ 1.38 = 97.5 n m
⎪ m = 1 ⇒ d 1 = ( 1 + 1/ 2 ) 538 n m / 2 ⋅ 1.38 = 292 n m
⎪ m = 2 ⇒ d 2 = ( 2 + 1/ 2 ) 538 n m / 2 ⋅ 1.38 = 487n m
In all cases the thickness of the film is less than the wavelength of the light. This makes it possible to ensure that the rays reflected on the anterior and posterior surface belong to the same wavefront and therefore guarantee coherence between them.
Answer:
Looking straight downward into a rain puddle whose surface is covered with a thin film of gasoline, you notice a swirling pattern of colors caused by interference inside the gasoline film. 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 about 541nm. What is the minimum possible thickness of the gasoline layer directly beneath you.
The answer is 98nm
Explanation:
Given that a thin film of gasoline (n = 1.38)
The wavelength of the green light = 541
Hence the condition for constructive interference
2t = (m + 1/2)λ/n
for thinnest layer m = 0
for the thickness
t = (λ/4n)
t = (541 × 10⁻⁹)/(4 × 1.38)
t = 98.007
t = 98nm
