Light — Speed, Reflection, Refraction & Spectrum

Light in physics is electromagnetic radiation. The main ideas students usually need are simple: light has a fixed speed in vacuum, it reflects at a surface, it refracts when it enters a new medium, and visible light is only a small part of the electromagnetic spectrum. In vacuum, light travels at

$$c \approx 3.00 \times 10^8\ \mathrm{m/s}$$

At a boundary, some of the light can reflect, some can refract, and some can do both, depending on the materials and the angle. Keep four ideas in mind:

• light has a definite speed in vacuum
• reflection means the ray stays in the same medium and bounces from a surface
• refraction means the ray enters a new medium and changes direction
• spectrum describes how light can be ordered by wavelength or frequency

The Core Relations And Their Symbols

In introductory physics, light is treated as an electromagnetic wave. In modern physics it also shows particle-like behavior, but for reflection, refraction, and the visible spectrum, the wave model is the one you need first. The vacuum relation is

$$c = \lambda f$$

where $\lambda$ is wavelength and $f$ is frequency, so a shorter wavelength means a higher frequency. That is why blue-violet visible light has a shorter wavelength than red. In a material, light usually travels more slowly:

$$v = \frac{c}{n}$$

where $n$ is the refractive index. The law of reflection is $\theta_i = \theta_r$, with both angles measured from the normal, not from the surface. Snell's law for refraction is

$$n_1 \sin \theta_1 = n_2 \sin \theta_2$$

Why Refraction Happens

Snell's law is not an arbitrary rule; it follows directly from the change in speed at the boundary. A light wave entering a higher-index medium slows from $c$ to $v = c/n$, but its frequency $f$ stays fixed, so its wavelength must shrink to $\lambda' = v/f$. Picture the wavefronts as a row of marchers crossing from pavement onto sand at an angle: the edge that reaches the slow medium first falls behind, so the whole line pivots. That pivot is the bend. Quantitatively, matching the wave crests along the boundary requires $n_1 \sin\theta_1 = n_2 \sin\theta_2$, which is exactly Snell's law. So the direction change is a geometric consequence of one side of the wave slowing before the other:

• enter a higher-index (slower) medium, and the ray bends toward the normal
• enter a lower-index (faster) medium, and it bends away from the normal, provided refraction still occurs

This also explains why frequency is treated as unchanged at the boundary while speed and wavelength adjust, and therefore why light from one source does not change color just because it entered glass.

Worked Example: Light From Air Into Glass

Suppose light goes from air into glass with

$$n_1 = 1.00, \qquad n_2 = 1.50, \qquad \theta_1 = 30^\circ$$

First find the speed in glass:

$$v = \frac{c}{n} = \frac{3.00 \times 10^8}{1.50} = 2.00 \times 10^8\ \mathrm{m/s}$$

Now the refracted angle with Snell's law:

$$1.00 \sin 30^\circ = 1.50 \sin \theta_2$$

Since $\sin 30^\circ = 0.5$,

$$0.5 = 1.50 \sin \theta_2 \quad\Rightarrow\quad \sin \theta_2 = \frac{1}{3}$$

and therefore

$$\theta_2 = \sin^{-1}\left(\frac{1}{3}\right) \approx 19.5^\circ$$

This makes physical sense: the light slows in glass and bends toward the normal because glass has the larger refractive index, exactly as the speed argument predicts.

Practice Check

Change the example from air-to-glass to glass-to-air or air-to-water and predict the bending direction before you calculate. If the new medium is faster, expect the ray to bend away from the normal; run Snell's law to confirm the angle.

Where The Colors Fit

The word "spectrum" can mean two related things. In the broad physics sense, the electromagnetic spectrum is the full range from radio waves to gamma rays, and visible light is only one narrow band inside it. In ordinary optics, the visible spectrum means the spread of visible wavelengths, often seen when white light passes through a prism or water droplets. Red light is at the longer-wavelength end of the visible range and violet at the shorter-wavelength end. The exact visible limits are not perfectly sharp, but a common rough range is about $400$ to $700\ \mathrm{nm}$ in vacuum.

Common Mistakes With Light Problems

• Treating visible light as all of light. Visible light is only one part of the electromagnetic spectrum.
• Measuring angles from the surface. Reflection and refraction angles are measured from the normal.
• Assuming light always bends toward the normal. That only happens when it enters a higher-index medium.
• Mixing up speed, frequency, and wavelength. In a medium, speed can change. At a boundary, introductory optics usually keeps the frequency the same and lets the wavelength change.

Where Reflection And Refraction Are Used

These ideas explain mirrors, eyeglasses, cameras, microscopes, rainbows, fiber optics, and many measurement tools. Even advanced optical systems build on the same core questions: how fast is the light moving here, and what happens when it meets a boundary?