Question

Calculate the minimum thickness of an oil slick on water that appears blue when illuminated by white light perpendicular to its surface. Take the blue wavelength to be 470 nm and the index of refraction of oil to be 1.40.

Answer 1

Answer:

t = 83.93 nm

Explanation:

given,

blue light wavelength (λ)= 470 nm

refractive index of oil (μ)= 1.40

minimum thickness of an oil slick on water = ?

using constructive interference formula

 now,

       $2 \mu t = (m + \dfrac{1}{2})\lambda$

   where, t is the thickness of the oil slick

     m = 0,1,2

for minimum thickness m = 0

       $2\times 1.40\times t = (0 + 0.5)\times 470$

       $2.8\times t = 235$

       $t = \dfrac{235}{2.8}$

             t = 83.93 nm

minimum thickness of an oil slick on water = t = 83.93 nm

Answer 2

The minimum thickness of an oil slick should be 83.93 nm

Important information:

Take the blue wavelength to be 470 nm and the index of refraction of oil to be 1.40

Calculation of the minimum thickness:

$2\times 1.40 \times t= (0 + 0.5) \times 470\\\\28 \times t = 235$

t = 83.93 nm

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