You know that it's safe to microwave plastic containers, since their molecules don't respond significantly to 2.4 -GHz microwaves. But since you've learned about thin-film interference, you worry about enhanced microwave intensity due to multiple reflections in plastic cookware. You calculate the minimum thickness for a plastic tray with refractive index 1.3 that will cause enhanced reflection of microwaves incident normal to the plate. Are your worries assuaged?

Microwave radiation belongs to the electromagnetic spectrum, which encompasses all forms of electromagnetic radiation, including visible light, radio waves, and X-rays. The unique property of microwaves is their behavior with various materials, especially how they are absorbed and reflected.

Frequency and wavelength define the characteristics of microwaves. In our case, we are dealing with 2.4 GHz microwaves, commonly used in microwave ovens to heat food. The frequency is quite high, leading to a relatively short wavelength even though they belong to the longer wavelength part of the spectrum. The relevance to our daily life is paramount; if microwaves are absorbed by water in our food, they can also affect other substances, potentially leading to safety concerns.

The refractive index is a dimensionless number that describes how fast light travels in a medium. It is defined as the ratio of the speed of light in a vacuum compared to the speed of light in the material. For the plastic tray in question, it has a refractive index of 1.3, meaning light, or in our case microwaves, travels 1.3 times slower in the plastic than in a vacuum.

This concept also plays a crucial role in thin-film interference, a phenomenon that occurs when light waves reflected by the upper and lower boundaries of a thin film interfere with one another. The refractive index impacts how much the wave is slowed and bent when entering the film, which ultimately influences the interference pattern. Microwaves, when encountering a material such as plastic, will also be subjected to this principle, potentially leading to hotspots if the plastic dimensions cause constructive interference of the waves.

Wavelength calculation is integral when dealing with any form of electromagnetic radiation, including microwaves. As mentioned in the solution, when microwaves transition from air to another medium, such as plastic, their speed and wavelength change. This wavelength transformation is critical in determining the behavior of microwaves as they encounter thin films—the plastic in this scenario.

The equation \(\lambda' = \frac{\lambda}{n}\) allows us to calculate the new wavelength within the material by adjusting for the refractive index. This new wavelength determines the constructive and destructive interference patterns within the plastic, which are essential for understanding the film's impact on microwave radiation intensity. Hence, correct wavelength calculation can help assess whether specific plastic thicknesses would amplify microwaves through interference, addressing concerns over microwave-safe materials.