What will be the fringe pattern if wedge shaped air film is illuminated with white light?

#### Solution

At the thin edge, t=0 hence path difference between the rays is `λ/2`, a condition for darkness. Hence the edge of the film appears dark. It is called as zero order band. That is the reason extensively thin film appears dark in reflected light. Beyond the edge for a thickness t for which path difference is λ, we obtain the first bright band. As t increases to a value for which path difference is `(3λ) / 2 `we obtain the first dark band.

For normal incidence and air film, r=0 and μ = 1

Total path difference = 2tcosθ + λ/2

2tcosθ = (2n-1) `λ/2`………………………… maxima

2tcosθ= nλ……………………………………....minima

For every small angle of wedge,

As θ=0, cosθ=1

2t= (2n-1) `λ/2`

2tcosθ= nλ

i.e. every next bright fringe will occur for thickness interval of λ/2 each

t=n `λ/2`, t=0, `λ/2`, 2 `λ/2`, 3`λ/2`,…………….

i.e. every next dark fringe will occur for thickness interval of `λ/2` each