A silicon monoxide (n = 1.45)film of 288.9 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 that is most efficiently transmitted, we need to use the formula:

mλ = 2nt + λ/2

where m is an integer (in this case we can assume m = 1 for the first transmission peak), λ is the wavelength of light, n is the refractive index of the lens (1.56), t is the thickness of the silicon monoxide film (288.9 nm), and we solve for λ.

Simplifying the equation gives:

λ = 2nt / (2n - 1)

Plugging in the values gives:

λ = 2(1.45)(288.9 nm) / (2(1.45) - 1) = 558.9 nm

Since this is in the visible region, the closest answer choice is C) 559 nm. Therefore, the correct answer is C.

A Silicon Monoxide (N = 1