Thin film appears red, thickness of this part?

In summary, there is a thin film of oil (n=1.5) floating on water, with a red (700nm) portion visible when looking directly at the film. To determine the thickness of this red part, we can use the equation mλf = 2d + λf/2, where m is an integer and λf is the wavelength of light inside the film. The statement of the problem is not clear about whether they want the minimum thickness, but based on the phrase "large portion of red", it is likely that they do. Therefore, we can choose m = 1 to get the smallest thickness, but we must also take into account that the wavelength of light inside the oil is shorter than in
  • #1
Cocoleia
295
4

Homework Statement


A thin film of oil (n=1.5) is floating on top of water. When looking directly at this film, a large portion appears red (700nm). What is the thickness of the red part of the layer?

Homework Equations

The Attempt at a Solution


Since n for oil > n for air, there will be a phase shift of lambda/2
There will be no phase shift for the next reflection, but it travels 2x the thickness of the film (2d)
Since it appears red, i said it was constructive interference. So we get mlambda = 2d + lambda/2
If they asked for minimum i would set m=0 and use the 700nm to solve for d, but they don't specify. What should i do?
 
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  • #2
You are right, there are different thicknesses (corresponding to different integer values of m) that would give constructive interference. I think they should have stated minimum thickness if that's what they wanted. The phrase "large portion of red" suggests that the thickness is very small, because with larger thicknesses the regions of interference maxima and minima tend to crowd together. But this still does not necessarily mean that you must pick the smallest thickness. So, I'm with you. The statement of the problem should have been clearer.

Note that if you choose m = 0 you will get a negative value for d. So, if you want the smallest thickness you would want to choose the smallest value of m for which you get a non-negative thickness.

Also, remember that lambda in the formula represents the wavelength of the light inside the film. So, you would not use 700 nm.
 
  • #3
Cocoleia said:
So we get mlambda = 2d + lambda/2
Not quite. You are forgetting that in the oil the wavelength is shorter than in air (or vacuum). Your expression does not take into account this fact.
 
  • #4
kuruman said:
Not quite. You are forgetting that in the oil the wavelength is shorter than in air (or vacuum). Your expression does not take into account this fact.
How would I find the correct wavelength?
 
  • #5
Cocoleia said:
How would I find the correct wavelength?
 
  • #6
TSny said:
Note that if you choose m = 0 you will get a negative value for d. So, if you want the smallest thickness you would want to choose the smallest value of m for which you get a non-negative thickness.
.
Can I choose m = 1 then? or will this no longer respect the conditions
 
  • #7
In your equation mλf = 2d +λf/2, any positive integer value of m would correspond to constructive interference. m = 1 seems like the most natural choice. It will give the smallest thickness.
 

FAQ: Thin film appears red, thickness of this part?

What causes a thin film to appear red?

The appearance of color in a thin film is due to the phenomenon of interference. When light waves reflect off the top and bottom surfaces of the film, they interfere with each other, resulting in some wavelengths being amplified and others being canceled out. The color we see is determined by which wavelengths are amplified.

How does the thickness of the film affect its color?

The thickness of a thin film plays a crucial role in determining its color. Thicker films will produce more distinct and saturated colors, while thinner films may appear more translucent or even colorless. This is because the thickness affects the interference pattern and the wavelengths that are amplified or canceled out.

Why does the color of a thin film change when viewed from different angles?

When we view a thin film from different angles, the path length that light travels through the film changes. This results in different interference patterns and therefore, a different color. This phenomenon is known as iridescence and is commonly seen in soap bubbles and oil slicks.

Can the color of a thin film be controlled or manipulated?

Yes, the color of a thin film can be controlled by adjusting its thickness, the angle of incident light, and the properties of the material it is made of. This is why we see a variety of colors in soap bubbles or on the wings of certain insects. Thin films are also used in various technological applications, such as anti-reflective coatings and color-changing displays.

Why do different thin films produce different colors?

The color produced by a thin film is dependent on its thickness, the angle of incident light, and the properties of the material. Therefore, different films made of different materials and with varying thicknesses will produce different colors. Additionally, the way light interacts with the material, such as whether it is transparent or absorbs certain wavelengths, will also affect the color produced.

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