What is the minimum thickness necessary for an antireflective coating (n=1.9) to be useful against incident light of 530 nm wavelength?

To determine the minimum thickness necessary for an antireflective coating effective against incident light of a specific wavelength, one must use the principle of destructive interference. Antireflective coatings are designed to reduce reflection and maximize transmission through a surface by causing reflections from various layers to interfere with each other.

For antireflective coatings, a quarter-wavelength optical thickness is optimal. The formula to calculate the minimum thickness of the coating is:

Thickness (t) = λ / (4n)

where λ is the wavelength of the incident light in the medium (which is air in this case, so it remains 530 nm) and n is the refractive index of the coating (1.9).

Calculating the thickness:

1. Convert the wavelength to the required medium:

λ = 530 nm.

2. Substitute the values into the formula:

t = 530 nm / (4 * 1.9)

t = 530 nm / 7.6

t = 69.7368 nm.

Rounding this value gives approximately 69.7 nm, confirming that this thickness will produce the desired effect of destructive interference for the light wavelength of 530 nm. By ensuring