interference

Interference Overview

  • Study of thin film interference, Newton’s rings, and their applications.

  • Types of coatings: anti-reflection and anti-transmission coatings.

Thin Parallel Film

Characteristics

  • Thickness is nearly equal to the wavelength of light (average wavelength: 5500Å or 0.55μm).

  • Examples: Oil films on roads during rain, soap bubbles.

Applications

  • Anti-reflection coatings on camera lenses.

  • Solar cells, interference filters, anti-reflection coatings on glass.

Reflected and Transmitted Systems

  • Definition of optical path and coherent rays.

  • Reflection and Refraction:

    • A monochromatic light beam strikes thin film at angle of incidence i.

    • Reflections occur at points A and B, leading to constructive/destructive interference at point C.

    • Bright appearance results from constructive interference; dark appearance from destructive interference.

Path Difference and Optical Path Length

  • Ray I travels a distance only to point D.

  • Ray II travels greater distance due to travel through a denser medium, affecting speed and optical path.

  • Stoke’s Law: Phase change during reflection in denser media affects interference pattern.

Path Difference Formula

  • Path difference between Ray I and Ray II determines intensity and brightness at point A.

Characteristics of Thin Film Interference

  1. Patterns of reflected and transmitted light are complementary.

  2. Condition for constructive interference: 2utcos(r) = 2n.

  3. Condition for destructive interference: 2utcos(r) + λ/2 = (2n + 1)λ.

Special Conditions

  • For extremely thin or thick films, interference patterns are not observed:

    • Thin (t << λ): No interference pattern.

    • Thick (t >> λ): Large path differences, inconsistent visibility.

Fizau's and Haidinger’s Fringes

Fizau’s Fringes

  • Thickness varies gradually; fringes appear horizontal and equidistant.

  • Alternating dark and bright fringes result from path difference (PD) variation along the film.

Haidinger’s Fringes

  • Constant thickness with varying angle of refraction.

  • Circular symmetry leads to concentric rings.

Color in Thin Films

  • Oil films and soap bubbles exhibit random colors due to varying thickness, angle, and refractive index in ambient light.

  • Colors vary regionally based on constructive and destructive interference conditions.

Wedge-Shaped Films

  • Ray I and II produce parallel fringes, demonstrating path differences relative to film edge.

Newton's Rings

  • Created using plano-convex lens and glass plate, producing rings of alternate colors due to coherent interference of reflected rays.

  • Characteristics:

    • Complementary patterns of reflected and transmitted rings.

    • Appearance of white light leads to colored fringes at center.

    • Various factors influence ring visibility: height, wavelength changes, and lens imperfections.

Coatings

Anti-Reflection Coatings

  • Thinner films designed for transmitted light to reduce reflection.

  • Optimal thickness produces destructive interference of reflected rays.

  • Common materials: MgF2 and SiO2.

Anti-Transmission Coatings

  • Denser workings that increase film reflectivity with constructive interference.

  • Used in mirror applications; materials include TiO2 and ZnS.