A silicon monoxide (n = 1.45)film of 112-nm thickness is used to coat a glass camera lens (n = 1.56).What wavelength of light in the visible region (390 to 710 nm)will be most efficiently transmitted by this system? (1 nm = 10−⁹ m)

Question

Quizplus · Accepted Answer

To find the wavelength of light most efficiently transmitted by the system, we need to find the wavelength where the reflection is minimized (i.e., the phase change upon reflection is 0).

For a light ray incident on a medium with index of refraction n1, and reflecting off a medium with index of refraction n2, the phase change upon reflection is given by:

Δϕ = 2π(n2-n1)d/λ

where d is the thickness of the film, and λ is the wavelength of light.

For minimum reflection, Δϕ should be an integer multiple of π, or:

Δϕ = mπ

where m is an integer.

For the given system, we want to minimize the reflection at the surface of the silicon monoxide film and the glass substrate, which means that we need to have two phase changes of π (i.e., m = 2). Thus:

2π(n2-n1)d/λ = 2π

Solving for λ, we get:

λ = 2d(n2-n1)

Plugging in the given values, we get:

λ = 2(112 nm)(1.56-1.45) = 650 nm

Therefore, the wavelength most efficiently transmitted by this system is 650 nm, which corresponds to the color red. The answer is D.

A Silicon Monoxide (N = 1