What is the Formula for Thin Film Interference?

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SUMMARY

The discussion centers on the formula for calculating thin film interference, specifically addressing destructive interference. The user calculated the film thickness by dividing the wavelength of light (425 nm) by 4, resulting in a thickness of 106 nm. Key concepts include the phase shift during reflection at boundaries of different optical densities, with a phase shift of π occurring when light reflects off a medium of higher optical density. The formulas for constructive and destructive interference are also provided, emphasizing the role of film thickness, refractive index, and angle of incidence.

PREREQUISITES
  • Understanding of thin film interference principles
  • Knowledge of optical density and phase shifts in light
  • Familiarity with the formulas for constructive and destructive interference
  • Basic concepts of wavelength and film thickness in optics
NEXT STEPS
  • Study the derivation of the thin film interference formulas
  • Learn about the impact of varying refractive indices on interference patterns
  • Explore practical applications of thin film interference in coatings and optics
  • Investigate experimental methods to measure film thickness using interference techniques
USEFUL FOR

Students in physics or optics courses, researchers in material science, and professionals working with optical coatings or thin film technologies will benefit from this discussion.

Precursor
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Homework Statement

[PLAIN]http://img403.imageshack.us/img403/2696/33095583.jpg

The attempt at a solution

I simply took 425 nm and divided it by 4 by using the destructive reflection from thin film. I got 106 nm as my answer, which is c. Is this correct?
 
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Precursor said:
I simply took 425 nm and divided it by 4 by using the destructive reflection from thin film.
What's your reasoning behind this?
 
remember your rules of reflection. when an electromagnetic wave is in incidence of a medium of higher optical density the light will have a phase shift of pi. If an electromagnetic wave is incidence on a less optically dense medium there is no shift.

contructive 2mpi = (4(pi)ntcos(x))/lambda -k + b

destructive (2q+1)pi = (4(pi)ntcos(x))/lambda -k + b

where is the phase shift due to the intial and main medium and b is the phase shift due to the main medium and final. x is the angle of incidence which would be 0 in your case. t is film thickness of main medium. n is the index. lambda is wavelength.
 

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