Thin film interference on pavement

[Kawrae]

A thin film of oil (n = 1.26) is located on a smooth, wet pavement. When viewed perpendicular to the pavement, the film appears to be predominantly red (640 nm) and has no component of wavelength 512 nm. How thick is the oil film?

I'm getting confused by the use of two wavelengths in this problem... I'm pretty sure I need to use the equation 2nt = (m+1/2)lambda and solve for t. But what wavelength do I use? I don't understand what it means when it says "...has no component of wavelength 512nm"

Can someone help me with this?

 

[ehild]

A thin film of oil (n = 1.26) is located on a smooth, wet pavement. When viewed perpendicular to the pavement, the film appears to be predominantly red (640 nm) and has no component of wavelength 512 nm. How thick is the oil film?

I'm getting confused by the use of two wavelengths in this problem... I'm pretty sure I need to use the equation 2nt = (m+1/2)lambda and solve for t. But what wavelength do I use? I don't understand what it means when it says "...has no component of wavelength 512nm"

Can someone help me with this?

There is constructive interference at 640 nm and destructive interference at 512 nm.

ehild

 

[wais]

Sure, let's break down the problem step by step. First, the equation you mentioned, 2nt = (m+1/2)lambda, is known as the thin film interference equation and is used to calculate the thickness of a thin film of a given refractive index when it is viewed perpendicularly. In this problem, we are given the refractive index of the oil (n = 1.26) and the wavelength of the red light (640 nm). We can use these values to solve for the thickness of the oil film.

However, the statement "has no component of wavelength 512 nm" is a bit confusing and may require some clarification. In thin film interference, the colors we see are a result of constructive and destructive interference of light waves of different wavelengths. The fact that there is no component of wavelength 512 nm means that there is no constructive interference happening at that specific wavelength, so we won't see any green light in the reflected light from the oil film.

Now, let's plug in the values we have into the thin film interference equation. We have n = 1.26, lambda = 640 nm, and m = 0 (since there is no constructive interference at 512 nm). This gives us:

2(1.26)t = (0+1/2)(640 nm)

Simplifying, we get:

2.52t = 320 nm

Dividing both sides by 2.52, we get:

t = 320 nm / 2.52 = 126.98 nm

So, the thickness of the oil film on the pavement is approximately 126.98 nm. Keep in mind that this calculation assumes that the oil film is uniform in thickness and that there are no other factors affecting the interference pattern. I hope this helps clarify the problem for you!