Find Optimal Wavelength for Thin Film Camera Lens Coated with Magnesium Fluoride

[rachiebaby17]

Homework Statement

A camera lens (n = 1.90) is coated with a thin film of magnesium fluoride (n = 1.40) of thickness 90.0 nm. What wavelength in the visible spectrum is most strongly transmitted through the film?

Homework Equations

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The Attempt at a Solution

I have no idea where to start, is there an equation that will use both n's at once?

 

[rl.bhat]

Search in Google for thin film interference.

 

[nlightner]

I would approach this problem by first understanding the concept of optical thin films and their behavior with different wavelengths of light. I would then use the thin film interference equation, which is based on the principle of constructive and destructive interference, to calculate the optimal wavelength for the given scenario. The equation is as follows:

2nt = (m + 1/2)λ

Where:
n = refractive index of the thin film
t = thickness of the thin film
m = order of the interference
λ = wavelength of light

In this case, the thin film is magnesium fluoride with a refractive index of 1.40 and a thickness of 90.0 nm. The refractive index of the camera lens is 1.90. We want to find the wavelength that will result in the strongest transmission through the film, which corresponds to the maximum value for m in the equation.

To solve for the optimal wavelength, we can rearrange the equation to:

λ = (2nt - (m + 1/2)) / m

We know that the maximum value for m is when the numerator is equal to 2nt, so we can plug in the values and solve for λ:

λ = (2 x 1.90 x 1.40 x 90.0 x 10^-9 m - (1 + 1/2)) / 1

= 0.504 μm

Therefore, the optimal wavelength for the camera lens coated with a thin film of magnesium fluoride is 0.504 μm, which falls in the green region of the visible spectrum. This means that green light will be most strongly transmitted through the film.

It is important to note that this calculation assumes a normal incidence of light on the film and does not take into account any absorption or scattering effects. In a real-world scenario, these factors may also affect the optimal wavelength. Additionally, the thickness of the thin film can also be adjusted to achieve maximum transmission at different wavelengths.