A certain crude oil has an index of refraction of 1.25 . A ship dumps 1 m 3 of this oil into the ocean and oil spreads into a thin uniform film on water surface (μ=(4/3)). When light of wavelength 500 nm is incident on it, the reflected light shows maxima. What is the area (in km 2 ) covered by the spilled oil ? Assume that the thickness of film is minimum required to satisfy this criterion.

Question

A certain crude oil has an index of refraction of 1.25 . A ship dumps 1 m 3 of this oil into the ocean and oil spreads into a thin uniform film on water surface (μ=(4/3)). When light of wavelength 500 nm is incident on it, the reflected light shows maxima. What is the area (in km 2 ) covered by the spilled oil ? Assume that the thickness of film is minimum required to satisfy this criterion. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

2 μ t = n λ=λ t =(λ/2 μ)=(500 × 10-9/2 × 1.25) =2 × 10-7 m 2 A =( V / t )=(1/2 × 10-7)=5 × 106 m 2 =5 km 2

2μt=nλ=λ t=2μλ​=2×1.25500×10−9​ =2×10−7m2 A=tV​=2×10−71​=5×106m2 =5km2

$2 μ t = nλ = λ$
$t = \frac{λ}{2 μ} = \frac{500 \times 1 0 ^{- 9}}{2 \times 1.25}$
$= 2 \times 1 0^{- 7} m^{2}$
$A = \frac{V}{t} = \frac{1}{2 \times 1 0 ^{- 7}} = 5 \times 1 0^{6} m^{2}$
$= 5 k m^{2}$