1. by Bhaskar Department of Physics K L University

2. Lecture 6 (18 Aug) Interference in Thin Films

3. Colours of thin films When a thin film is exposed to white light such as sun light, beautiful colours appear in the reflected light. Ex: soap bubble and thin oil film Soap Bubble: Let us assume thickness of thin film t is constant 2 μ t cos r, μ and r are the variables. White light has varying λ, μ also varies with λ. Curved Nature of soap bubble – angle of incidence varies for different colours – angle of refraction varies 2 μ t cos r =(n+1/2) λ --> varies with μ and r Satisfies the condition constructive Interference at particular λ

4. Thin Film: Angle of Incidence (i) and angle of refraction (r) will remain constant. But for different λ values μ varies and also the thickness of the film t may not be constant. No dark band is seen because if a particular point satisfies condition for destructive interference for a particular wavelength, At the same point may satisfy condition for constructive interference for different wavelength and hence throughout the film we see multicolours.

5. NON-REFLECTIVE COATINGS: If film is between layers with higher and lower refractive index, conditions reverse Get 180° phase change at both reflections  Condition for Maxima 2 μ t = n λ n = 0, 1, 2 …  Condition for Minima 2 μ t = (2n+1) λ/2 n = 0, 1, 2 …

6. NON-REFLECTIVE COATINGS:  The Fresnel’s Law I r /I  Non-reflecting medium can prepared by coating the thin films on to the mediums.  These films were useful to prevent the reflection of light.

8. Phasor Addition of Waves Phasor Addition of Waves:

9. Phasor Addition of Waves EθEθ

10. Three-Slit Interference Pattern

11. Phasors for Several Waves The resultant phasor, E R, is the vector sum of the individual phasors. The resultant phasor, E R, is the vector sum of the individual phasors. The phase angle β is the phase angle between E R and the first phasor. The phase angle β is the phase angle between E R and the first phasor. E

12. 12

13. 13