Designing a Reddish-Orange Office Tower: Calculating Film Thickness

[crosbykins]

Homework Statement

A construction company designs a new office tower with an outer surface mostly made of glass(n glass = 1.52). The company wishes that the glass appear a reddish-orange without having to use coloured glass. Instead, a thin film (n film = 1.65) is used that maximizes the reflection of that colour of light (wavelength 615 nm). What thickness would this film need to be?

Homework Equations

n coating = wavelength glass/wavelenght coating

The Attempt at a Solution

wavelength coating = (615 * 10^-9)/(1.65)
= 3.73 * 10^-7 m

t = 3.73 * 10^-7 m/4
= 9.32 * 10^-8 m

****I really don't think this is right, could someone help me out with a step-by-step solution. Thank you so much! :)

 

[anathema]

I would first start by confirming the information given in the problem and making sure I understand the question. The problem states that the construction company wants the glass to appear a reddish-orange color without using colored glass. This means that the glass must be transparent and the color must come from some other source. The company has decided to use a thin film with a refractive index of 1.65 to achieve this color.

Next, I would identify any relevant equations that could help me solve this problem. In this case, the equation for thin film interference is appropriate, which is:

n coating = wavelength glass/wavelength coating

Where n coating is the refractive index of the thin film, wavelength glass is the desired wavelength of light, and wavelength coating is the wavelength of light in the thin film.

Now, I would plug in the given values into the equation and solve for the thickness of the film:

n coating = wavelength glass/wavelength coating
1.65 = 615 * 10^-9 m/wavelength coating
wavelength coating = 615 * 10^-9 m/1.65
wavelength coating = 3.73 * 10^-7 m

Since the wavelength in the thin film is equal to the wavelength in air divided by the refractive index of the thin film, we can solve for the thickness of the film by dividing the wavelength in the thin film by 4 (since the film is sandwiched between two glass layers):

t = 3.73 * 10^-7 m/4
t = 9.32 * 10^-8 m

Therefore, the thickness of the thin film needed to achieve the desired reddish-orange color is approximately 9.32 * 10^-8 meters. This means that the light must travel through this thickness of film before it is reflected back, creating the desired color. It is important to note that this calculation assumes perfect conditions and may not be entirely accurate in real-life situations. I would also consider factors such as the angle of incidence and the properties of the glass itself, which could affect the final result.