Thin Film Interference

1. Thin Film Interference

2. What is a thin film? A thin film is a thin layer of material that has a different index of refraction than its surroundings. Thin films cause incident light to undergo interference (constructive or destructive, depending on the wavelength of the light and the thickness of the film). Thin film interference is responsible for all of the colors that appear in soap bubbles and oil slicks.

3. When light is incident on a thin film, part of the incident light is reflected off of the top of the film, and part is transmitted into the film and reflected off of the bottom! It is the interference of these two reflected rays that we will see when we look into the film. incident ray reflected ray 2 reflected ray 1 air soap t = thickness of the film air

4. In reality, the light makes many, many reflections in the film! incident ray reflected ray 3 reflected ray 4 reflected ray 2 reflected ray 1 t However, we only need to analyze the first two reflected rays in order to make predictions about the interference pattern.

5. There are two types of thin films Type I: Oil slick type (fast-slow-slower) low n air high n oil higher n ground Type II: Bubble type (fast-slow-fast) low n air high n soap low n air

6. Type I: Oil Slick Type Light is incident upon the oil from the air. It is partially transmitted into the oil, and partially reflected back into the air. The light in the oil reflects off of the ground, and refracts back out into the air. As a result, we have multiple rays coming toward our eyes that started from the same incident ray! 1 2 air (n = 1.0) oil (n ≈ 1.5) t ground (very high n)

7. The most important concept of thin film inteference If rays 1 and 2 are in phase with one another, then there will be constructive interference. You will be able to see that wavelength of light from the surface of the film. If rays 1 and 2 are out of phase with one another, then there will be destructive interference. You will not be able to see the wavelength of light from the surface of the film. 1 2 air (n = 1.0) oil (n ≈ 1.5) t ground (very high n)

8. The waves start out in phase, but travel different path lengths by the time that they are superimposed Wave 2 travels an extra distance of ≈ 2t! 1 2 air (n = 1.0) oil (n ≈ 1.5) t ground (very high n)

9. However… when a wave (even light) is reflected off of a different medium, it may invert, depending on the density of the medium! Let’s review how this works. air (n = 1.0) oil (n ≈ 1.5)

10. Boundary Reflections: Revisited When a wave reflects off of a more dense medium than the one in which it is traveling, it will become inverted. This is called a 180° phase change.

11. This same principle applies to light reflecting off of a medium with a higher refractive index. Less dense More dense 180° phase flip – trough becomes a crest, or vice versa

12. Type I Thin Films: Oil Slick 1 2 air (n = 1.0) oil (n ≈ 1.5) t ground (very high n) At which interface(s) does the reflecting light undergo a phase flip?

13. At which interface(s) does the reflecting light undergo a phase flip? At both! When the light reflects off of the oil from the air, it is phase flipped. When the transmitted ray reflects off of the ground at the bottom of the oil, it is also phase flipped! 1 2 air (n = 1.0) oil (n ≈ 1.5) ground (very high n) Since both of the waves that are interfering have undergone a 180° phase flip, the net result is the same as if neither of the waves did!

14. A summary so far The waves start out in phase. Both parts undergo phase flips at some point (so it is mathematically the same as if neither one did). Wave 2 travels an extra distance of ≈ 2t 1 2 air (n = 1.0) oil (n ≈ 1.5) t ground (very high n)

15. And now for the grand finale The waves started out in phase, but one of them went some extra distance. In order for them to constructively interfere, they must be back in phase when they are superimposed. Does this sound familiar? Constructive interference must satisfy the equation Where L1 is the distance traveled by the wave reflected off of the top of the film, and L2 is the distance traveled by the wave reflected off of the bottom of the film m = 0 if the waves have traveled the same distance, m = 1 if one of the waves has traveled one extra wavelength, m = 2 if one of the waves have traveled two extra wavelengths, etc.

16. The end result! Wave 2 has traveled an extra distance of ≈ 2t. This gives the end result 1 2 t for constructive interference in a type I thin film.

17. And, for destructive interference… in a Type I thin film (low-high-higher)