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Chapter 25: Problem 16

A thin film of oil \((n=1.50)\) is spread over a puddle of water \((n=1.33) .\) In a region where the film looks red from directly above $(\lambda=630 \mathrm{nm}),$ what is the minimum possible thickness of the film? (tutorial: thin film).

Short Answer

Expert verified
Answer: The minimum thickness of the oil film is 210 nm.

Step by step solution

01

Understand thin film interference

Thin film interference occurs when light waves reflect off two surfaces separated by a thin film, causing constructive or destructive interference between the reflected waves. In this case, the film is the oil on top of the water. Constructive interference leads to a brighter color, while destructive interference results in a darker color.
02

Find the interference condition for a minimum thickness

We will use the following equation for the constructive interference of the thin film: $$2nt = m\lambda_{air}$$ where \(n\) is the refractive index of the oil, \(t\) is the film thickness, \(m\) is an integer representing the order of constructive interference, and \(\lambda_{air}\) is the wavelength of light in air. In our case, \(n=1.50\), \(\lambda_{air}=630\,\text{nm}\), and we want to find the smallest possible \(t\) for constructive interference, so we will consider the case when \(m=1\).
03

Solve for the minimum thickness of the film

Plug in the given values and solve for \(t\): $$2(1.50)t = 1(630\,\text{nm})$$ $$t = \frac{630\,\text{nm}}{2(1.50)}$$ $$t = 210\,\text{nm}$$ Therefore, the minimum possible thickness of the film for it to appear red when viewed from above is 210 nm.

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Most popular questions from this chapter

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