Thin film interference occurs when light waves reflect off the top and bottom surfaces of a thin film, causing constructive or destructive interference. This interference results in colorful patterns that depend on the film thickness and material. Constructive interference occurs when the film thickness is an integer multiple of half the wavelength, while destructive interference happens when the thickness is an integer plus half a wavelength. The phase of reflected light also shifts depending on whether the film's refractive index is smaller or larger than the medium below.

1. THIN FILM INTERFERENCE
Selina Lo
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2. DEFINITION
• interference of light waves reflecting off the top surface of a film with the
waves reflecting from the bottom surface
• if the thickness of the film is on the order of the wavelength of light, then
colorful patterns can be obtained
• constructive and destructive interference of reflected light waves causes the
colorful patterns we often observe in thin films (Ex: soap bubbles and layers
of oil on water)

3. FORMULAS
Constructive interference
• 2*nt = (m)λn where m = 0,1,2,…,
Destructive interference
• 2*nt = (m+½)λn where m = 0,1,2,…,

4. PHASE SHIFT
• when Na is smaller than Nb, phase shift of π (half a wavelength) will occur

5. EXAMPLES
Question:
A thin film of a material is floating on water (n = 1.33). The material has a refractive
index of n = 1.20, the film looks bright in reflected light as the thickness approaches
0. But when the material has a refractive index of n = 1.45, the film looks black in
reflected light as the thickness approaches 0. Explain these observations in terms of
constructive and destructive interference and the phase changes that occur when
light waves undergo reflection.
Solution:
If the refractive index of the film is greater than the water below, the phase shift of the
ray traveling through the film and reflecting off the interface between the film and the
water is 0. If the refractive index of the film is smaller than that of water the phase shift
of the ray traveling through the film and reflecting off the interface between the film
and the water is π. Both reflected rays will have the same phase and as the film
thickness approaches 0, they are in phase and the material will look bright.

6. EXAMPLES
• Let λ = 518 n = 1.26 (soap + water)
λ1.26 = (518)/(1.26) = 411.1 nm
Min. Intensity: d = (1/2)m λ, m = 1,2,3,…
d = (1/2) 1*(411.1 nm) = 205.6 nm
d = (1/2) 2*(411.1 nm) = 411.1 nm
d = (1/2) 3*(411.1 nm) = 616.7 nm
Max. Intensity: d = (1/2)*(m+(1/2)) λ, m = 1,2,3,…
d = (1/2)*(1+(1/2))*411.1 nm = 308.3 nm
d = (1/2)*(2+(1/2))*411.1 nm = 513.9 nm
d = (1/2)*(3+(1/2))*411.1 nm = 719.4 nm

7. BIBLIOGRAPHY
• Thin-film interference. Retrieved March 22, 2015, from
http://labman.phys.utk.edu/phys222core/modules/m9/Thin films.htm
• Hawks, R.,Iqbal, J. Mansour, F, Milner-Bolotin, M. & Williams P. 2014. Physics for
Scientists and Engineers: An Interactive Approach (1st ed.) Nelson Education
Ltd.