For constructive interference, 2nt = (m + ½)λ where n = refractive index of film t
Rainbows The slightly wedge shape of the oil film means that the reflected waves from the bottom surface each have slightly different path lengths to travel before recombining with the reflected waves from the top surface. The result is that some colours will recombine in- phase at some places, producing regions bright in that colour, while at other places that same colour will be suppressed due to destructive interference.
Thin air Wedges Consider two glass slides placed with a piece of paper between them at one end: Fringes are seen from above. If we assume that the slides are coated so that no reflection occurs at the top of the top slide or bottom of the bottom slide, this is essentially like a thin film (of air) but of varying thickness. θ D L Air wedge
Consider light of wavelength λ incident from above: Some light reflects at the bottom of the top slide and some at the top of the bottom slide. Q. What will the phase change be at these boundaries? So if they are to interfere constructively what must the path difference be? θ
Now consider light incident vertically from above a point where the slide separation is d: For constructive interference to occur vertically above this point... 2d = (m + ½) λ i.e. Bright fringes will occur at d = λ, 3λ, 5λ etc θ d
Therefore there will be equal fringe separation x as shown below... From the small triangle below m=1 and m=2: From the original diagram: Thus the fringe spacing (of equal thickness x) is given by: (The thickness of the paper could thus be determined from x) θ = λ 2x θ = D L x = λL 2D m = 0 m = 1 m = 2 d = 3λ 4 d = 5λ 4 λ2λ2 xx
Practical Measuring the thickness of a human hair using thin-wedge interference