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

The refractive index of a substance is a measure of how much that substance can bend or refract light as it passes through. In educational terms, think of it like a straw in a glass of water — the straw looks bent at the point where it enters the water due to refraction. Toluene, a common organic solvent, has a refractive index of 1.49, which is an intrinsic property of this chemical.

This value plays a significant role in the study of light interactions known as thin film interference, which can be strikingly observed in soap bubbles or oil slicks. It's crucial for students working on physics problems to record this value correctly, as it is often given in the problem statement and is vital for calculating the optical properties of materials and phenomena such as the thickness of films that result in colorful interference patterns.

To get a practical sense of how this refractive index affects light behavior, if light were traveling from air into toluene, it would slow down and change direction slightly, leading to observable effects like the colorful patterns mentioned or the precise calculation of film thickness in an interference scenario.

Optical path difference (OPD) is a foundational concept in the study of wave optics, especially when delving into the phenomena of interference. The OPD calculates the difference in the distance light waves travel, which can lead to constructive or destructive interference patterns. The path difference becomes especially noticeable when light waves reflect off materials with different refractive indices.

In the context of thin film interference, like that of a toluene film, the OPD is determined by the thickness of the film and the refractive index. For light reflecting off the bottom surface of a film, it travels a longer optical path than a wave reflecting off the top surface, due to the additional distance within the film where the light speed is slower. This difference can cause a phase shift that affects how the light waves overlap and interfere.

To calculate the actual OPD, one can use the formula: OPD = 2nt, where 'n' is the refractive index of the film, and 't' is the thickness of the film. This calculation is essential for determining the specific conditions where constructive interference maximizes reflection at particular wavelengths, leading to bright bands or colors.

Reflection of specific wavelengths due to thin film interference is responsible for the brilliant color displays seen in soap bubbles or oil films on water. Wavelength reflection is the distance between successive peaks of a wave, and this distance determines the color of the light. For example, a wavelength of roughly 460 nm is in the blue-violet spectrum visible to the human eyes.

When light hits a thin film, certain wavelengths of light are reflected more strongly due to constructive interference when the OPD equals a whole multiple of the wavelength. For destructive interference, when the light waves are out of phase and cancel each other, those specific wavelengths are diminished or completely missing from the reflected light, thus altering the color that we perceive.

The exercise example provided required finding the minimum film thickness for the strongest reflection of a 460 nm wavelength. The key takeaway for students is that certain thicknesses of thin films result in specific colors being strongly reflected due to this type of interference. Recognizing this connection between thin film thickness, refractive index, and wavelength reflection is crucial for solving problems on this topic and understanding how interference filters and anti-reflective coatings work.