A uniform plane wave is normally incident onto a slab of glass \((n=1.45)\) whose back surface is in contact with a perfect conductor. Determine the reflective phase shift at the front surface of the glass if the glass thickness is (a) \(\lambda / 2 ;(b) \lambda / 4 ;(c) \lambda / 8\).

Imagine light as a collection of waves spreading out from a source. A uniform plane wave is a simplification used to describe these waves when they travel through space without any disturbance — meaning they have a constant amplitude and frequency and their wavefronts (the peaks and valleys of the waves) are infinite, flat planes.

Picture a perfectly calm ocean with waves that are all the same size and move together side by side without changing shape. This is similar to how uniform plane waves behave. They are a useful concept in physics because they make it easier to predict how light and other forms of electromagnetic radiation will behave under certain conditions, like when they strike a surface.

When light enters a different material, such as glass, it changes speed and direction. This bending of light is known as refraction. The glass refractive index, denoted as n, is a number that tells us how much the light will bend.

The refractive index of glass (around 1.45 for common glass) is a way of saying that light travels about 1.45 times slower in glass than it does in a vacuum. A higher refractive index indicates that the light is significantly slower, causing a larger bend. This property is fundamental in optics, affecting how lenses focus light and how prisms create spectrums.

Conductors are materials that allow electrons to move freely. A perfect conductor is an idealized material where the electrons move with no resistance at all; in other words, it has an infinite electrical conductivity. When an electromagnetic wave encounters a perfect conductor, it can't penetrate the surface and is completely reflected. This is known as the perfect conductor boundary condition.

In practice, no material is a perfect conductor, but some materials like superconductors come very close under certain conditions. The boundary condition is vital for understanding how waves behave when encountering different materials and is used in designing antennas and other radio frequency devices.

When two or more waves meet while traveling through the same medium, they affect each other's displacement. This phenomenon is called wave interference. There are two main types of interference: constructive, where waves add up to make a larger wave, and destructive, where they cancel each other out to make a smaller wave or no wave at all.

An everyday example of wave interference is the patterns seen when two sets of ripples cross each other in a pond. When applied to light, interference is responsible for the colorful patterns in soap bubbles and oil on water. It's also the principle behind technologies such as noise-cancelling headphones.