Understanding Light Waves at an Air-Glass Boundary

When light waves travel from one medium to another, such as from air to glass, they interact with the new medium. This interaction causes some of the light to be reflected back into the original medium (air), while some of the light passes into the new medium (glass) and changes direction, a phenomenon called refraction.

The question asks about a property of the light wave that remains the same for both the incident wave (in air) and the refracted wave (in glass). Let's consider the properties mentioned:

Properties of Light Waves and Medium Change

• Speed: The speed of light changes when it moves from one medium to another. Light travels fastest in a vacuum, slightly slower in air, and significantly slower in denser media like glass. The change in speed is what causes refraction.
• Direction: The direction of light changes during refraction unless the light hits the boundary perpendicularly. It also changes during reflection. So, the direction is generally not the same.
• Brightness: Brightness is related to the intensity or amplitude of the wave. When light hits a boundary, some energy is reflected, and some is refracted. Therefore, the intensity of the refracted wave is less than the intensity of the incident wave, assuming no energy loss in the media. Thus, the brightness changes.
• Frequency: The frequency of a light wave is determined by the source of the light (e.g., the oscillations of electrons in a lamp). It represents the number of wave crests passing a point per second. When a wave passes from one medium to another, the rate at which the wave crests arrive at the boundary is the same as the rate at which they leave the boundary to enter the new medium. Therefore, the frequency of the wave does not change.

The relationship between the speed of a wave ($v$), its frequency ($f$), and its wavelength ($\lambda$) is given by the equation:

$\qquad v = f\lambda$

When light passes from air to glass, its speed ($v$) changes. Since the frequency ($f$) remains constant, the wavelength ($\lambda$) must also change to satisfy this equation. Specifically, because the speed decreases in glass (compared to air), the wavelength also decreases.

Why Frequency is Constant During Refraction

Think about the interface between the two media. Wave crests arrive at the interface from the air side at a certain rate (the frequency). These crests then cause disturbances in the glass medium, generating wave crests there. The rate at which crests arrive must equal the rate at which they leave into the glass. If the frequency changed, it would imply either wave crests are disappearing or being created at the boundary, which is not what happens. The source determines the frequency, and this property is conserved as the wave propagates through different media.

Here's a summary of how properties change:

Based on this analysis, the only property listed that remains the same for the incident wave in air and the refracted wave in glass is the frequency.

Revision Table: Light Wave Properties at Boundary

• Speed changes (decreases from air to glass).
• Direction changes (due to refraction).
• Brightness/Intensity changes (some light is reflected).
• Frequency remains constant.
• Wavelength changes (decreases from air to glass because speed decreases and frequency is constant).

Additional Information: Refractive Index and Wave Properties

The change in the speed of light when it enters a medium is quantified by the medium's refractive index ($n$). The refractive index is defined as the ratio of the speed of light in vacuum ($c$) to the speed of light in the medium ($v_{medium}$):

$\qquad n = \frac{c}{v_{medium}}$

For air, $n_{air}$ is approximately 1. For glass, $n_{glass}$ is typically around 1.5. Since $n_{glass} > n_{air}$, it follows that $v_{glass} < v_{air}$.

Using the wave equation $v = f\lambda$, and knowing that frequency ($f$) is constant:

• In air: $v_{air} = f\lambda_{air}$
• In glass: $v_{glass} = f\lambda_{glass}$

Since $v_{glass} < v_{air}$ and $f$ is constant, it must be true that $\lambda_{glass} < \lambda_{air}$. This confirms that both speed and wavelength change, while frequency stays the same.