Solve Thin-Film Equations: Red Light on Oil in Water

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In summary, the reflected red light has a wavelength of 615 nm in air and the oil has a thickness of 2.640e-7 m, and by plugging these values into the formula for constructive interference, we can solve for the refractive index of the oil. This gives us a value of 0.58239, which is lower than the refractive index of water, indicating that the speed of light in the oil is indeed faster than in water.
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r_swayze
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Homework Statement



White light illuminates an oil film on water. Viewing it directly from above, it looks red. Assume that the reflected red light has a wavelength of 615 nm in air, and that the oil has a thickness of 2.640e-7 m. What is the refractive index of the oil? Assume that the refractive index of water is greater than that of the oil.

Homework Equations



2nt = (m+1/2) λ

The Attempt at a Solution



2nt = (m+1/2) λ

n = 1/2 λ/(2t) = 1/2 (615e-9)/(2*2.64e-7)

n = 0.58239

I don't know why this answer is wrong. The problem seems to be straight forward, just plug in the numbers into formula right?

If m is greater than 0 then the answer n comes out higher then the refraction index of water, 1.33, so m has to be 0 I presume?

Edit: Never mind, figured it out.
 
Last edited:
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how you figured this out? can i know?
 
  • #3
A refractive index less than 1 implies that the speed of light in that medium would be faster than the speed of light in vacuum!

To solve this example, you just need to consider the constructive interference condition, and couple that with Snell's Law.
 

1. What are thin-film equations and why are they important?

Thin-film equations are mathematical models used to describe the behavior of thin films, which are layers of liquid or gas with a thickness of a few micrometers or less. These equations are important because they can help us understand and predict the physical properties and behavior of thin films, which have a wide range of applications in industries such as optics, coatings, and electronics.

2. What is the role of red light in thin-film equations for oil in water systems?

Red light is a specific wavelength of light that is often used in thin-film equations for oil in water systems. This is because red light has a longer wavelength compared to other colors, making it more sensitive to changes in the thickness and refractive index of the thin film. This allows for more accurate measurements and calculations in these systems.

3. How do you solve thin-film equations for red light on oil in water?

To solve thin-film equations for red light on oil in water systems, you will need to use a combination of mathematical and experimental techniques. This may include applying boundary conditions, using the Fresnel equations, and measuring the reflectance and transmittance of the thin film at different angles and wavelengths.

4. What factors can affect the accuracy of thin-film equations for red light on oil in water?

Several factors can affect the accuracy of thin-film equations for red light on oil in water systems. These include the optical properties of the materials involved, the thickness and uniformity of the thin film, and external factors such as temperature and humidity. It is important to carefully control and measure these factors to ensure accurate results.

5. What are some real-world applications of solving thin-film equations for red light on oil in water?

Solving thin-film equations for red light on oil in water has a wide range of practical applications. These include designing and optimizing anti-reflective coatings for lenses and solar panels, controlling the color and appearance of thin films in the food and cosmetic industries, and developing new technologies for optical sensors and displays. Understanding and accurately predicting the behavior of these systems is crucial for their successful application in these industries.

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