Animated Solution for Physics - Optics: When a ray of light enters a glass slab from air

Imagine a ray of light traveling freely through the air, suddenly striking the surface of a glass slab. As it crosses this boundary, it bends towards the normal, a phenomenon we know as refraction. But beyond the bending of the path, what happens to the fundamental properties of the light wave itself? Does it speed up? Does its color change? Let's dive into the physics of a wave crossing optical boundaries.

To understand the behavior of light, we must rely on the fundamental wave equation. For any wave, the speed $v$ is the product of its frequency $f$ and its wavelength $\lambda$:

This simple yet profound equation holds the key to unlocking what happens during refraction. When light moves from air into glass, the properties $v$, $f$, and $\lambda$ are put to the test.

Constancy of Frequency

Here is the most crucial concept to remember in optics: Frequency is a property of the source.

When an electron oscillates and emits a photon, the frequency of that photon is permanently locked in. It is the heartbeat of the wave. Whether the light is traveling through the vacuum of space, the Earth's atmosphere, or a dense block of glass, its frequency $f$ remains absolutely constant.

While frequency is stubborn, the speed of light is highly adaptable. The speed of light in a medium depends on the optical density (refractive index, $n$) of that medium. Glass is optically denser than air ($n_{\mathrm{glass}}>n_{\mathrm{air}}$).

When light enters the glass, it interacts with the densely packed atoms, effectively slowing down its propagation through the material. Therefore, the velocity of the light decreases:

Wavelength Decreases

Now, let's bring it all together using our wave equation. We can rearrange it to solve for wavelength:

We have established two facts: the frequency $f$ is a constant, and the velocity $v$ decreases as light enters the glass. Mathematically, if the numerator ($v$) decreases while the denominator ($f$) stays the same, the overall value of the fraction must decrease.

Therefore, the wavelength $\lambda$ must decrease to keep the equation balanced. Physically, you can imagine the wavefronts getting squished closer together as they hit the 'traffic jam' of the denser glass medium.

When a ray of light enters a glass slab from air, its velocity decreases, its wavelength decreases, but its frequency remains unchanged. And because the human eye perceives color based on frequency, the color of the light remains exactly the same inside the glass. Always remember to lock the frequency when changing media!