A beam of light traveling through a piece of glass emerges into air. Which of the following statements is true as the light exits the glass? i. The speed of light stays the same; ii. The light speeds up; iii. The light slows down; iv. The frequency of the light stays the same; v. The frequency of the light increases; vi. The frequency of the light decreases; vii. The wavelength of the light stays the same; viii. The wavelength of the light increases; ix. The wavelength of the light decreases. (A) i, iv, vii (B) i, v and vii (C) ii, iv and viii (D) ii, v, ix (E) iii, iv and ix

When we talk about the speed of light, many of us immediately think of the constant speed it travels in a vacuum - roughly 299,792 kilometers per second. However, this speed changes when light moves through different materials. Each material has a property known as the refractive index, which determines how much the light slows down as compared to its speed in a vacuum.

The refractive index is a ratio of the speed of light in a vacuum to its speed in the given medium. Glass, water, and air each have their unique refractive indices. For instance, air has a refractive index very close to 1, meaning the speed of light is nearly the same in air as it is in a vacuum. On the other hand, glass's refractive index is higher, around 1.5, which indicates the light travels slower in glass compared to air.

As light transitions from a denser medium (with a higher refractive index, like glass) to a less dense medium (with a lower refractive index, like air), it speeds up. This phenomenon is at the core of many optical technologies, such as lenses and prisms, which manipulate light to create images or split light into its component colors.

Frequency is a fundamental characteristic of light, often described as the number of wave crests that pass a given point per unit of time. It is measured in units called hertz (Hz). Unlike the speed of light, the frequency is determined by the source of the light and remains constant, regardless of the medium through which the light is travelling.

Whether light is moving through a vacuum, air, water, or glass, its frequency doesn't change. When light encounters a material interface and is refracted, the transition doesn't affect its intrinsic oscillation rate. This means that the color of the light, which is directly related to its frequency, remains the same as the light moves between materials. It's this sturdiness of frequency that is integral in preserving the color of an image as light passes through various media, a key aspect in photography and vision.

Wavelength can be pictured as the distance between successive peaks of a light wave. Unlike frequency, the wavelength does change depending on the medium through which the light is traveling. This is because the speed of light changes in different mediums, but the frequency, determined solely by the light's source, does not.

In a denser medium such as glass, where the speed of light is slower, the wavelength is shorter. When light moves into a less dense medium like air, where it can travel faster, the wavelength becomes longer. The relationship between speed, frequency, and wavelength can be captured by the equation \[ v = f \lambda \], where \(v\) represents the speed of light, \(f\) is the frequency, and \(\lambda\) is the wavelength. This concept plays a pivotal role in fields like spectrometry and astronomy, where understanding the changes in wavelength helps scientists infer vital information about the properties of substances and celestial objects.