Question

Calculate the minimum thickness (in nm) of an oil slick on water that appears blue when illuminated by white light perpendicular to its surface. Take the blue wavelength to be 480 nm and the index of refraction of oil to be 1.43.

Answer 1

The minimum thickness = 83.92 nm

Step-by-step explanation:

The relation between the wavelength in a particular medium and refractive index
`\lambda_n = ( \lambda )/(n)`

where ;

`\lambda` = wavelength of the light in vacuum

n = refractive index of medium with respect to vacuum

For one phase change :

`2t = (\lambda_n)/(2)\\\\where \ \lambda_n = (\lambda)/(n)\\\\Then \ \\\\2t = (\lambda)/(2n)\\\\t = (\lambda_n)/(4n)`

Replacing 1.43 for n and 480 nm for λ; we have:

`t = (480)/(4(1.43))`

t = 83.92 nm

Thus; the minimum thickness = 83.92 nm