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Chapter 32: Problem 44

A thin film of toluene \((n=1.49)\) floats on water. Find the minimum film thickness if the most strongly reflected light has wavelength \(460 \mathrm{nm}\).

Short Answer

Expert verified
The minimum thickness of the toluene film for which the most strongly reflected light occurs is approximately \(154.36 nm\).

Step by step solution

01

Understanding the Given Information

In the given problem, the strongly reflected light's wavelength, \(位\), is \(460 nm\) and the refractive index of toluene, \(n\), is \(1.49\). We have to find the minimum thickness for which this light is most strongly reflected.
02

Find the Order of Interference

For minimum thickness, the reflected light must undergo constructive interference. The condition for constructive interference (bright fringe) in thin film interference is given by \(2nt = m位\), where \(n\) is the refractive index of the medium, \(t\) is the thickness of the film, \(m\) is the order of interference (an integer), and \(位\) is the wavelength of light. For minimum thickness, \(m = 1\).
03

Calculate the Minimum Thickness

Consequently, using the formula \(2nt = 位\), we can isolate \(t\) and calculate the film's minimum thickness: \(t = 位 / (2n) = 460 nm / (2 * 1.49) = 154.36 nm\) (approximately).

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