Understanding Parallel Thin Film Interference

May 30, 2025

Parallel Thin Film Lecture Notes

Introduction to Optical Path

  • Optical path = Refractive index (渭) 脳 Geometrical path
  • In air, 渭 = 1, so optical path = geometrical path

Overview of Parallel Thin Film

  • Thin film could be glass or other materials
  • Refractive index of the medium = 渭; thickness = d
  • Surrounding both sides with air (渭 = 1)

Interference Pattern in Reflected Light

  • Incident ray partially reflected & refracted at the film interface
  • At the second interface, more reflections and transmissions occur
  • Focus on amplitude division interference
  • Ray A1 (from incident ray) and Ray A2 (reflected ray) interfere

Path Difference Calculation

  • Angle of incidence (I) remains the same for both rays
  • Up to point A, both rays travel equal distances
  • Rays become parallel beyond point A, traveling equal distances to the screen

Path Difference Formula

  • Path difference (螖) = 渭 脳 (AB + BC) - AD
  • Ray 1 travels AD in air (渭 = 1), Ray 2 travels in medium (渭)

Trigonometry and Geometry

  • Use triangles to express distances in terms of thickness (d) and angles (R, I)
  • For triangles ABE and CBE:
    • AB = d 脳 sec(R)
    • BC = d 脳 sec(R)
    • AD = 2 脳 AE (from congruent triangles)

Final Path Difference Expression

  • Substitute AE and AC into 螖:
  • 螖 = 2渭d sec(R) - 2d 脳 (渭 脳 sin(R))
  • Simplifies to incorporate refractive index into calculations

Conditions for Interference

  • Maxima: Path difference = n位 (integral multiples of 位)
  • Minima: Path difference = (n - 1/2)位
  • The additional term of 卤位/2 accounts for phase change upon reflection
  • When light reflects from denser to rarer, there鈥檚 no phase change

Fringes of Equal Inclination

  • Changes in angle of incidence affect path difference and hence interference pattern observed
  • These are termed as fringes of equal inclination due to their reliance on angle changes

Interference Pattern in Transmitted Light

  • Ray 3 (transmitted) and Ray 4 (reflected) also interfere
  • Analyses similar to reflected light but results differ due to energy conservation

Case of Wedge-Shaped Thin Films

  • When thickness is not uniform, leading to wedge-shaped films
  • Similar conditions apply, but angle 伪 affects cosine in path difference equations
  • Maxima and minima conditions are similar to parallel thin films with adjustments for angle 伪

Key Takeaways on Wedge-Shaped Films

  • Points of contact (thickness = 0) yield dark rings based on path difference equations
  • Understanding the relationship between thickness, angles, and light behavior is critical in interference phenomena

Conclusion

  • Interference patterns provide insights into optical properties of thin films
  • Importance of precise calculations and understanding underlying physics in optics.

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