(Solved): 1. Advanced Thin Films: Finding the thickness of a piece paper. A wedge-shaped film of air is made ...

1. Advanced Thin Films: Finding the thickness of a piece paper. A wedge-shaped film of air is made by placing a small piece of paper between the edges of two flat pieces of glass as shown in the diagram (which is not scale). Light of wavelength $$500\mathrm{nm}$$ is incident normally on the glass plates and interference fringes are observed by reflection. Diagram is not to scale, thickness of paper $$<L$$ (a) Draw a careful diagram of the plates showing the approximate path of light for the incident angle shown in the diagram. Label the surfaces where there is a $$180^{?}$$ phase shift. (NOTE: The actual angle of incidence is $$0^{?}$$, but the angle of incidence shown more clearly shows the reflection of light.) (b) Derive an equation for the condition of destructive interference in terms of the angle $$?$$. Solve your equation for the number of dark fringes per centimeter, $$m/x$$, where $$m$$ is an integer and $$x$$ is the location of a dark fringe. Label any variables on the diagram you drew in part (a), including $$x$$. (c) You observe 16 dark lines per centimeter. What is the thickness of the paper?