Lecture on Wavelengths and Thin Film Interference

Key Concepts

• Wavelengths in Different Media:

  • Light travels through different media with different wavelengths.
  • Wavelength in the air is denoted as lambda A.
  • Wavelength in the oil (or thin film) is denoted as lambda B.
  • The wavelength in the oil is crucial for calculations in thin film interference.

• Path Difference and Interference:

  • Light traveling through a thin film can emerge constructively or destructively, depending on the phase difference.
  • Constructive interference occurs when waves emerge in phase, while destructive interference occurs when they emerge out of phase (180 degrees).

Calculating Wavelengths

• Frequency and Speed Relationship:

  • Frequency remains constant across media changes.
  • Speed of a wave = Wavelength x Frequency.
  • Wavelength in a new medium can be calculated using the ratio of the speed of light in different media.

• Formula for Wavelength in a Thin Film:

  • Use:
    • [ \text{Wavelength in B} = \left( \frac{V_B}{V_A} \right) \times \text{Wavelength in A} ]
  • If given the index of refraction (N):
    • [ \text{Wavelength in B} = \left( \frac{N_A}{N_B} \right) \times \text{Wavelength in A} ]

Conditions for Constructive and Destructive Interference

• Constructive Interference:

  • 2T = M (integer) x [ \text{Wavelength in Thin Film} ]
  • In terms of speed or index of refraction:
    • [ \frac{V_B}{V_A} \times \text{Lambda A} ]
    • [ \frac{N_A}{N_B} \times \text{Lambda A} ]

• Destructive Interference:

  • 2T = [ (M + \frac{1}{2}) \times \text{Wavelength in Thin Film} ]
  • Similar formula adjustments apply.

• Pi Shift Consideration:

  • A pi shift in one wave changes interference conditions.

Simplification for Air

• If region A is air (N=1), formulas simplify:
  • Constructive: [ M \times \frac{\text{Lambda A}}{N_B} ]
  • Destructive: [ (M + \frac{1}{2}) \times \frac{\text{Lambda A}}{N_B} ]

Applications and Special Cases

• Thin Film Thickness:
  • If the film thickness is zero (or negligible), interference depends on whether there is a pi shift.
• Anti-Reflective Coating:
  • Used to make reflected light waves destructive.

Conclusion

• Thin film interference can be a complex topic, but understanding these principles helps in mastering the problem-solving process.