1. by Bhaskar Department of Physics
Engineering Physics by
Bhaskar
Department of Physics
K L University

2. Interference in Thin Films
Lecture 4&5 (06,07 & 13 Aug)
Interference in Thin Films

3. Interference in thin films
Types of Interference: The phenomenon is divided into two classes based on the mode of production of interference. These are
Interference produced by the division of wave front
Young’s double slit experiment.
Interference produced by the division of amplitude
But interference pattern can also be produced by division of amplitude of a single wave.
Lloyd’s mirror.
But the positions of the dark and bright fringes are reversed here when compared to the patterns of Young’s double slit experiment.

4. Interference in thin films
Stocks Principle: According to stocks principle an wave undergoes a phase change of 180 degrees on reflection from a medium of higher index of refraction than the one in which it is travelling.

5. Interference in thin films
Reflection of a Transverse Wave from a Fixed End:
Wave exerts upward force on support
=> downward force on rope
=> inversion of original wave

6. Interference in thin films
Reflection of a Transverse Wave from a Free End:
If end is free to move wave is not inverted
No force on free end
So wave is just reflected

7. Interference in thin films
Reflection by denser medium
Reflection by less dense medium

8. Interference in thin films
This reflection produces a phase difference of ½λ from the original wave and is called a fixed-end reflection.

9. Interference in thin films
The reflection produces no phase difference with the original wave, this is called a free-end reflection.

10. B denser medium rarer A C O ar at a ar2 D art A denser medium rarer A
att|
atr|
M VENKAT

11. Interference in thin films
Optical Path:
The optical path travelled by a light ray in a medium of refractive index 'μ' is not equal to actual path travel led by the light ray.
Optical path travelled by light beam ǂ Actual path travelled by light

12. Interference in thin films
Thin film planes can be parallel to each other or inclined. That is why, the concept of interference in thin films can be studied under two categories, namely,
Interference in parallel plate film and
Interference in wedge-shaped films.
Soap Film – Why Color?

13. Interference in thin films
We observes colors in such thin films as soap bubbles, coatings on camera lenses and in a butterfly's wings or peacock's feathers. 
When ray 1 strikes the top interface, some of the light is partially reflected, ray 2, and the rest is refracted, ray 3. 
When ray 3 strikes the bottom interface, some of it is reflected, ray 4, and the remainder is refracted, ray 6.
When ray 4 strikes the top interface from underneath, some is reflected (not shown) and some is refracted, ray 5. 
It is the interference between rays 2 and 5 that produces a thin film's color when the film is viewed from above.

14. Interference in thin films
Interference in plane parallel films due to reflection of light:
Ray 2 undergoes a phase change of 180° with respect to the incident ray
Ray 1, which is reflected from the lower surface, undergoes no phase change with respect to the incident wave

15. Interference in thin films
Interference in plane parallel films due to reflection of light: T N S Q i i
air i C r A r t M E B t r P

16. Interference in thin films
Interference in plane parallel films due to reflection of light:
For constructive interference
2 μ t cos r =(2n±1) λ/2 n = 0, 1, 2 …
For normal incidence r=00
2 μ t = (2n±1) λ/2 n = 0, 1, 2 …
For destruction interference
2 μ t cos r = n λ n = 0, 1, 2 …
For normal incidence r=0°
2 μ t = n λ n = 0, 1, 2 …

17. Interference in thin films
Two factors influence interference
Possible phase reversals on reflection
Differences in travel distance
The conditions are valid if the medium above the top surface is the same as the medium below the bottom surface
If the thin film is between two different media, one of lower index than the film and one of higher index, the conditions for constructive and destructive interference are reversed

18. Interference in thin films
Interference in plane parallel films due to transmitted of light:
The conditions for bright is
2 μ d cos r = n λ n = 0, 1, 2 …
The conditions for dark is
2 μ d cos r =(2n±1) λ/2
n = 0, 1, 2 …
We can say the interference pattern due to reflected and transmitted rays are complementary each other.

19. Interference in thin films
Interference in wedge-shaped films:

20. Interference in thin films
Interference in wedge-shaped films:
For constructive interference
2 μ t cos (r + α) =(2n±1) λ/2 n = 0, 1, 2 …
For normal incidence r=00
2 μ t cos α = (2n±1) λ/2 n = 0, 1, 2 …
For destruction interference
2 μ t cos (r + α) = n λ n = 0, 1, 2 …
2 μ t cos α = n λ n = 0, 1, 2 …

21. Interference in thin films
Applications of Wedge method:
Determination of thickness of a paper or diameter of a wire/hair.
2) Verification of flatness of the given transparent surface.

22. Interference in thin films
Determination of thickness of paper or thin film:

23. Interference in thin films
Determination of thickness of paper or thin film:
Thickness of paper:

24. Interference in thin films
Ray 2: No phase change from internal reflection BUT wave travels extra distance 2 t during which wavelength is
number of “extra” wavelengths from travel through the film is
• Ray 1: 180° (i.e. π) phase change from external reflection
equivalent to a path difference of

25. Interference in thin films
NON-REFLECTIVE COATINGS:
If film is between layers with higher and lower refractive index, conditions reverse
constructive interference for
2 μ t = n λ n = 0, 1, 2 …
Get 180° phase change at both reflections

26. Interference in thin films
NON-REFLECTIVE COATINGS:
Non-reflecting medium can prepared by coating the thin films on to the mediums.
These films were useful to prevent the reflection of light(still some light can reflects but reflected ratio decreases).
Here the condition for reflection minimum requires a path difference is λ/2.

27. Interference in thin films
NEWTON'S RINGS: