Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

An oil drop of RI = 1.2 floats on the water surface having RI = 1.33. The drop thickness is almost zero towards its edges but gradually increases towards the middle of the drop. In the reflected system, will the edge of the drop appear bright or dark? At what thickness of the drop will the light of $\lambda = 4800 \mathring{A}$ be strongly reflected in the $3^{rd}$ order?

i) The thinnest region of the drop corresponds to a bright region because both the reflected rays, one from the boundary between air and oil and another from boundary between oil and water are in phase hence condition for brightness is satisfied.

Δ=2μtcos(r+ϴ) ± $\frac{λ}{2}$ ± $\frac{λ}{2}$.

i.e Δ=2μtcos(r+ϴ) ± λ

At the edge thickness is zero so condition of brightness is satisfied.

ii) For brightness, 2μtcos(r+ϴ) ± λ = nλ

2μ t cos r = nλ

For normal incidence cos r = 1

2μ t = nλ

n =3, λ= 4800 AU, μ =1.2

Thickness t= 6000 AU