# C 2001 Wiley, Physics Cutnell & Johnson 5 th Ed. Fig. 27–10 THIN-FILM INTERFERENCE When light shines on a thin film of oil floating on a layer of water,

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C 2001 Wiley, Physics Cutnell & Johnson 5 th Ed. Fig. 27–10 THIN-FILM INTERFERENCE When light shines on a thin film of oil floating on a layer of water, two light waves (#1 and #2), enter the eye after reflection and refraction. The oil thickness t = several n ’s of light in the oil oil = vac / n  path = 2t

C 2001 Wiley, Physics Cutnell & Johnson 5 th Ed. Fig. 27–11 NOTE: When a wave on a rope reflects from a wall, the wave undergoes a 180 o phase change. Light waves can also undergo a 180 o phase shift upon reflection depending on the reflecting surfaces.

The 180 o phase change depends on: 1.When light travels from a larger to a smaller index of refractive index, there is NO phase change upon reflection. 2. When light travels from a smaller to a larger index of refractive index, there is a 180 o phase change upon reflection. Larger to a smaller index NO phase change Smaller to a larger index 180 o phase change

C 2001 Wiley, Physics Cutnell & Johnson 5 th Ed. THIN-FILM INTERFERENCE There is NO phase change at air – oil interface. There is 180 o phase change at oil – water interface. oil = vac / n 180 o 0o0o  path = 2t

If there are no phase changes upon reflection constructive (max intensity) interference will occur if the top film (oil) is: 2 t = m n 2t = oil, 2 oil, 3 oil, … If there is a 180 o phase change upon reflection constructive (max intensity) interference will occur if top film (oil) is 2 t = (m + ½) n 2t + oil /2 = oil, 2 oil, 3 oil, … IMPORTANT: oil = vac / n For destructive (min intensity) interference, interchange the two equations!

If there are no phase changes upon reflection destructive (min intensity) interference will occur if top film (oil) is: 2 t = (m + ½) n 2t = ½ oil, 1.5 oil, 2.5 oil, 3.5 oil, … If there is a 180 o phase change upon reflection destructive (min intensity) interference will occur if top film (oil) is: 2 t = m n 2t + oil /2 = oil /2, 3 oil /2, 5 oil /2, … IMPORTANT: oil = vac / n

Fig. 37-12 Upper figures: Light waves striking an interface between optical materials at (approximately) normal incidence. Mechanical wave pulses on ropes: NO PHASE NO REFLECTION 180 o PHASE CHANGE CHANGE n a > n b n a = n b n a < n b

Fig. 37-15 A nonreflective coating has an index of refraction that is intermediate between those of glass and air. Destructive interference* occurs upon reflection when film thickness is ¼ in the film. *No reflected light here! n = 1.00 1.38 1.50 180 o

Fig. 37-16 A schematic diagram of a Michelson interferometer.

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