Thin film interference reflection

In summary, to achieve a reflection minimum for normal-incidence light of both 400 and 600 nm wavelength, a coating of 1.27 material should be added to 1.50 glass with a thickness of 472 nm. This thickness will also result in a reflection minimum at a wavelength between 400 and 600 nm, with a path difference of n(lambda)/2.
  • #1
meaowwuff
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Homework Statement


A coating of n1 = 1.27 material is to be added to n2 = 1.50 glass, in order to make it "irridescent."
a) What is the thinnest layer of material which will have a reflection maximum for normal-incidence light at BOTH 400 and 600 nm (vacuum) wavelength?
b) This thickness will have a reflection minimum at some wavelength between 400 and 600 nm. What is the wavelength of the reflection minimum?

2. Homework Equations

2*d=lambda(coating), 2*d=lambda(coating)/2

The Attempt at a Solution



I got the first part correct and the answer was 472 nm but I can't get b right. For b I did 2*d=lambda(coating)/2 since it says that the reflection will be minimum.
 
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  • #2

2. Homework Equations

2*d=lambda(coating), 2*d=lambda(coating)/2

The Attempt at a Solution



I got the first part correct and the answer was 472 nm but I can't get b right. For b I did 2*d=lambda(coating)/2 since it says that the reflection will be minimum.[/QUOTE]

In order to get minimum reflectance, the path difference between the directly reflected wave and that, which reflects from the glass-layer interface has to be odd number times half of lambda(coating) .
 
  • #3
Destructive interference occurs at ##2d =\lambda/2##, but also at other path differences...
 
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  • #4
In your problem light moves from low u to high u.reflection minimum means the part of incident rays reflected will suffer destructive interference .hence 2ud=n(lambda).
 
  • #5
Can you please help me with this problem?For the second part, you can use the equation for the phase shift in thin film interference:

Δφ = (2π/λ) * (n2*d*cosθ)

where Δφ is the phase shift, λ is the wavelength, n2 is the refractive index of the glass, d is the thickness of the coating, and θ is the angle of incidence (which is normal in this case).

For a reflection minimum, the phase shift should be an odd multiple of π, so we can set Δφ = π.

π = (2π/λ) * (1.50*d*cos0)

π = (2π/λ) * (1.50*d)

Solving for d, we get:

d = λ/3

Substituting the given wavelengths of 400 nm and 600 nm, we get:

d = 400 nm/3 = 133.33 nm
d = 600 nm/3 = 200 nm

So, the reflection minimum will occur at a thickness of 133.33 nm or 200 nm. We can also find the corresponding wavelengths using the first equation:

λ = (2*d)/2 = d = 133.33 nm
λ = (2*d)/2 = d = 200 nm

Therefore, the wavelength of the reflection minimum will be either 133.33 nm or 200 nm.
 

1. What is thin film interference reflection?

Thin film interference reflection is a phenomenon in which light waves reflecting off the top and bottom surfaces of a thin film interfere with each other, resulting in either constructive or destructive interference. This leads to the appearance of different colors or patterns on the film.

2. How does thin film interference reflection occur?

Thin film interference reflection occurs when light waves reflect off the top and bottom surfaces of a thin film with different refractive indices. This causes the waves to travel different distances and interfere with each other, resulting in the observed interference pattern.

3. What factors affect thin film interference reflection?

The thickness and refractive index of the thin film, as well as the angle of incidence and the wavelength of the incident light, all affect the interference pattern in thin film interference reflection. Changes in these factors can result in different colors or patterns being observed.

4. What are some real-world applications of thin film interference reflection?

Thin film interference reflection is used in various applications such as anti-reflective coatings on glasses or camera lenses, optical filters, and color-changing coatings on cars. It is also important in understanding the colors seen in soap bubbles and oil slicks.

5. How is thin film interference reflection different from thin film interference transmission?

Thin film interference reflection occurs when light waves reflect off the top and bottom surfaces of a thin film, while thin film interference transmission occurs when light passes through a thin film and reflects off the bottom surface. The interference patterns observed in these two cases are slightly different due to the different paths the light waves take.

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