Calculating the Longest Visible Wavelength for Thin Film Interference

In summary, an oil film with an index of refraction of 1.48 and a thickness of 360.0 nm floating on water with an index of refraction of 1.33 is illuminated from above by white light at normal incidence. The longest visible wavelength that will be strongly reflected is 456.24 nm, while the longest visible wavelength that will be strongly transmitted is 480.0 nm. The equation for reflectance is R=((n2-n1)/(n2+n1))^2, and when the thickness of the film is 1/4λ, the reflectance is minimum.
  • #1
hayowazzup
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Homework Statement


An oil film (index of refraction no = 1.48) floating on water (index of refraction nw = 1.33) is illuminated from above by white light at normal incidence. The film is 360.0 nm thick.



What is the longest visible wavelength that will be strongly reflected?

What is the longest visible wavelength that will be strongly transmitted?

Homework Equations



2nt = (m + 1/2)λ--constructive
2tn = m λ, with m = 0,1,2,...

The Attempt at a Solution


since visible range=400 - 700 nanometers
the longest visible wavelength for constructive interference ...should it be λ=2t/(2+1/2)
λ=456.24?
and so for the second question i use the second equation?
 
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  • #2
Do you know the equation for reflectance? I think if the thickness of the film is 1/4λ then the reflectance is minimum.
 
  • #3
R= ((n2-n1)/(n2+n1))^2
is it this one?
 

FAQ: Calculating the Longest Visible Wavelength for Thin Film Interference

What is thin film interference?

Thin film interference is a phenomenon that occurs when light waves reflect off two different surfaces of a thin film of a transparent material, such as glass or oil. The waves overlap and interfere with each other, resulting in a change in the color or intensity of the reflected light.

What causes thin film interference?

Thin film interference is caused by the difference in the refractive index of the two surfaces of the thin film. When light waves pass through a medium with a different refractive index, they change speed and direction, leading to interference when the waves recombine at the second surface.

How does the thickness of the thin film affect interference?

The thickness of the thin film plays a crucial role in thin film interference. When the thickness of the film is equal to the wavelength of the light, constructive interference occurs, resulting in bright colors. However, if the thickness is not an exact multiple of the wavelength, destructive interference occurs, producing dark colors.

What is the difference between constructive and destructive interference in thin films?

Constructive interference occurs when the waves from the two surfaces of the thin film are in phase, resulting in a brighter and more intense reflection. Destructive interference happens when the waves are out of phase, leading to a darker or even no reflection at all.

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

Thin film interference is utilized in many practical applications, such as anti-reflection coatings on glasses and camera lenses, color-changing pigments in cosmetics, and the production of holograms. It also plays a crucial role in the functioning of optical devices, such as thin-film interference filters and mirrors.

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