Question

In this problem, use 485 nm for the wavelength of blue light and the index of refraction of oil to be 1.40.

Calculate the minimum thickness (in nanometers) of an oil slick on water that appears blue when illuminated by white light that is incident perpendicular to the oil's surface.

Answer 1

The minimum thickness of the oil slick is 174.6 nm.

Step-by-step explanation:

When white light passes through a thin film, such as an oil slick on water, some of the light is reflected and some is transmitted. The reflected light undergoes constructive or destructive interference, depending on the thickness of the film. In this case, we are looking for the minimum thickness of the oil slick to appear blue when illuminated by white light.

To calculate the minimum thickness, we can use the equation for constructive interference in thin films:

2nt = mλ

Where:

• n is the index of refraction of the oil slick (1.4)
• t is the thickness of the oil slick
• m is the order of the interference (in this case, m = 1 for the first order)
• λ is the wavelength of the blue light (485 nm)

Plugging in the values, we get:

2 * 1.40 * t = 1 * 485 nm

Simplifying the equation, we find that the minimum thickness of the oil slick is 174.6 nm.