Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

A drop of liquid of volume 0.2 cc spreads uniformly over the surface of tank water of area $1 m^2$. The reflected spectrum of white light that is incident normally on the surface found to contain a $1^st$ order dark band of $λ = 5500 \mathring{A}$ in air. Find $\mu_{liq}$ if $\mu_{liq}\gt\mu_{water}.$

Volume = 0.2 cc, area = 100 sq cm, therefore thickness t= $\frac{V}{A}$, n=1

Thickness $t= \frac{0.2}{(100)^2} = 2 \times 10^{-5}$ cm

For dark bands 2μ t cos r = nλ

For normal incidence cos r = 1

Therefore $ μ = \frac{nλ}{2t} = \frac{1 \times 5500 \times 10^{-8}}{2 \times 2 \times 10^{-5}} =1.375$