Question

an oil slick on water is 116 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, in nanometers), given its index of refraction is 1.42? (assume the index of refraction of water is 1.33.)

Answer 1

The color that the oil will appear in is violet-blue.

Constructive interference of waves

The color of light that is most constructively reflected from the oil slick can be determined using the equation for constructive interference in thin films:

`\[ 2nL = m\lambda \]`

where:

• n is the refractive index of the material (oil),
• L is the thickness of the film,
• m is the order of the interference,
• lambda is the wavelength of light.

In this case, n for oil is 1.42, L given as 116 nm, and is the order of the interference (we'll consider m = 1 ) for the first-order maximum).

Rearranging the equation for wavelength:

`\[ \lambda = (2nL)/(m) \]`

Substitute the values:

`\[ \lambda = (2 * 1.42 * 116)/(1) \]`

`\[ \lambda \approx 329.12 \, \text{nm} \]`

So, the most constructively reflected wavelength, and thus the color that would be most intense, is approximately 329.12 nm. This corresponds to violet-blue light.