THIN FILM INTERFERENCE Selina Lo

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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)

FORMULAS

Constructive interference

• 2*nt = (m)λn where m = 0,1,2,…,

Destructive interference

• 2*nt = (m+½)λn where m = 0,1,2,…,

PHASE SHIFT

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

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.

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

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.