Problem: An oil slick on the water is 120 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength), given its index of refraction is 1.40?

FREE Expert Solution

Constructive interference is witnessed when:

$\overline{){\mathbf{2}}{\mathbf{t}}{\mathbf{=}}\frac{{\mathbf{\lambda }}_{\mathbf{n}}}{\mathbf{2}}{\mathbf{,}}\frac{\mathbf{3}{\mathbf{\lambda }}_{\mathbf{n}}}{\mathbf{2}}{\mathbf{,}}\frac{\mathbf{5}{\mathbf{\lambda }}_{\mathbf{n}}}{\mathbf{2}}{\mathbf{,}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}}$, where t is the thickness of the slock and λn is the wavelength of light in the medium.

Wavelength in a particular medium is related to refractive index by:

$\overline{){{\mathbf{\lambda }}}_{{\mathbf{n}}}{\mathbf{=}}\frac{\mathbf{\lambda }}{\mathbf{\eta }}}$, where λ is the wavelength of light in a vacuum and η is the refractive index of the medium.

91% (267 ratings)
Problem Details

An oil slick on the water is 120 nm thick and illuminated by white light incident perpendicular to its surface. What color does the oil appear (what is the most constructively reflected wavelength), given its index of refraction is 1.40?