LECTURE 13 THIN FILM INTERFERENCE. Instructor: Kazumi Tolich

Transcription

1 LECTURE 13 THIN FILM INTERFERENCE Instructor: Kazumi Tolich

2 Lecture Thin film interference Interference of reflected light waves Thin films of air The colors of soap bubbles and oil slicks

3 17.4 Thin-film interference Thin-film interference is the interference of light waves reflected from two boundaries of a thin film. Thin-films are used for antireflection coatings on camera lenses, microscopes, and other optical equipment. The bright colors of oil slicks and soap bubbles are also due to thin-film interference. Without anti-reflective coating With anti-reflective coating

4 17.4 Interference of reflected light waves A light wave is partially reflected from any boundary between two transparent media with different indices of refraction. The light is partially reflected not only from the front surface of a sheet of glass, but also from the back surface as it exits the glass into air. This leads to two reflections. v " v # > v " v " Two-string boundary analogy

5 Quiz: Light is shone from above on a thin piece of glass. Which of the following is/are correct about Ray 1 and Ray 2? Choose all that apply. A. Ray 1 has a % -phase shift of upon reflection. # B. Ray 1 has no phase shift of upon reflection. C. Ray 2 has a % -phase shift of upon reflection. # D. Ray 2 has no phase shift of upon reflection. air glass air Ray 1 Ray 2

6 Quiz: answer 6 Ray 1 has a % -phase shift of upon reflection. # Ray 2 has no phase shift of upon reflection. A light wave undergoes a phase change if it reflects from a boundary at which the index of refraction increases. n '() 1.0 < n /0' air glass air Ray 1 Ray 2 v # > v " v # < v " v " v " v # < v " v # > v " v " v "

7 17.4 Interference of reflected light waves For a thin, transparent film, most of the light is transmitted into the film. Light reflected off the surfaces interfere.

8 Quiz: Magnesium fluoride (MgF 2 ) is often used as an antireflection coating on lenses. Light is incident normally on the surface of MgF 2 although the diagram shows rays at an angle to show the details. The MgF 2 film is applied to the glass as an anti-reflective coating. Which of the following statements is correct? A. Ray R # and Ray R 4 constructively interfere. B. Ray R # and Ray R 4 destructively interfere. C. Ray R " and Ray R 5 constructively interfere. D. Ray R " and Ray R 5 destructively interfere.

9 Quiz: answer 9 Ray R # and Ray R 4 destructively interfere. Ray R " and Ray R 5 constructively interfere. Since the purpose of antireflection coating is to reduce the reflected light, Ray R # and Ray R 4 should destructively interfere. In that case, Ray R " and Ray R 5 should constructively interfere. Otherwise, the energy carried by the incident light simply disappears, which does not conserve energy.

10 Quiz: Light is incident normally on the surface of MgF 2 although the diagram shows rays at an angle to show the details. The indices of refraction of MgF 2 and glass are 1.38 and Which of the following is/are correct? Choose all that apply. A. Ray R # undergoes a % -phase shift upon reflection # B. Ray R # undergoes no phase shift upon reflection C. Ray R 4 undergoes a % -phase shift upon reflection # D. Ray R 4 undergoes no phase shift upon reflection

11 Quiz: answer 11 Ray R # undergoes a % -phase shift upon reflection # Ray R 4 undergoes a % -phase shift upon reflection # Since index of refraction of air is smaller than that of MgF 2, Ray R # undergoes a % -phase shift. # Since index of refraction of MgF 2 is smaller than that of glass, Ray R 4 undergoes a % -phase shift. # So there is not any relative shift of phase due to reflections alone. Phase shifts come from the path length difference.

12 Quiz: Light is incident normally on the surface of MgF 2 although the diagram shows rays at an angle to show the details. If the thickness of the MgF 2 coating is t, what is the path length difference between Ray R # and Ray R 4, in terms of t? t

13 Quiz: answer 13 2t Ray R 4 travels extra t to reach the MgF 2 -glass boundary, and another t to come back to the air- MgF 2 boundary. t

14 Quiz: Light is incident normally on the surface of MgF 2 coating although the diagram shows rays at an angle to show the details. The frequency of the incident light is f = "4 Hz. What is the wavelength of the light in nm inside the MgF 2 coating with an index of refraction of 1.38?

15 Quiz: answer 15 The atoms absorb and reradiate the light at the same frequency. In different media, the speeds of light are different, so the wavelengths of light of the same frequency are different as well, λ = vt = C D. The wavelength in vacuum is λ E'FAA> = G D. λ >?@(A> = C D = H I D = G = 5.K "K L > 1 JD ".5N O.NN "K PQ RS = 370 nm In general, λ >?@(A> = " J λ E'FAA>

16 Example: The indices of refraction of MgF 2 and glass are 1.38 and Light is incident normally on the surface of MgF 2 although the diagram shows rays at an angle to show the details. What is the thinnest film thickness of MgF 2 that works on an antireflection coating for light with a frequency of f = "4 Hz (near the center of the visible spectrum)?

17 17.4 Interference of reflected light waves / Demo The thin film interference conditions for constructive interference with 0 or 2 reflective phase changes or destructive interference with 1 reflective phase change: 2t = m % J m = 0, 1, 2, The thin film interference conditions for destructive interference with 0 or 2 reflective phase changes or constructive interference with 1 reflective phase change: 2t = m + " # % J m = 0, 1, 2, Demo: Dichroic filter

18 Quiz: A film with thickness t gives constructive interference for the reflected rays for light with a wavelength in the film of λ \(0>. How much thicker would the film need to be in order to give destructive interference? A. 2 λ \(0> B. λ \(0> C. λ \(0> 2 D. λ \(0> 4 t

19 Quiz: λ \(0> 4 The effective path length difference (including phase shifts due to reflection if any) before the change is an integer multiple of λ \(0> as the reflected rays constructively interfere. We need to add λ \(0> 2 to the effective path length difference. The phase shifts due to reflection if any do not change by changing the thickness of the film as the indices of refraction remain the same. By increasing the thickness by λ \(0> 4, the path length difference of the round trip increases by λ \(0> 2. t

20 17.4 Thin films of air / Demo A thin film of air can produce thin-film interference patterns. Demo: Newton s rings The thickness of the air is smaller toward the center of the lens. At the center the path length difference is nearly zero, and the rays interfere mostly destructively due to one % -phase shift upon # reflection.

21 17.4 The colors of soap bubbles and oil slicks / Demo The bright colors of soap bubbles or oil slicks on water are due to thin-film interference of white light. For a soap bubble, the light reflecting at the front surface of the bubble (the air-water boundary) undergoes a phase change, but the back reflection does not. air water λ 2 Demo: Soap film interference air

22 Example: A sheet of glass having an index of refraction of 1.40 is to be coated with a film of material having a refractive index of 1.55 such that green light with a wavelength of 525 nm is preferentially transmitted. a) What is the minimum thickness of the film that will achieve this result? b) Why are other parts of the visible light spectrum not also preferentially transmitted? c) Will the transmission of any color be sharply reduced? If so, which color?