Velocity of Light
Simple Explanation
Light travels at approximately 3 × 10⁸ m/s in a vacuum — the fastest speed at which any information or matter can travel, according to modern physics. Like any wave, its speed relates to its frequency and wavelength.
Why Do We Need It?
The speed of light is a fundamental constant of the universe, underlying not just optics but also modern physics topics like special relativity (covered in a later chapter).
Formula
Wave Speed Relation (for Light)
c = fλ
Like any wave, light's speed equals the product of its frequency and wavelength.
- c
- — Speed of light (in vacuum, ≈ 3 × 10⁸ m/s)
- f
- — Frequency of the light, in Hz
- λ
- — Wavelength of the light, in metres
When to use it: Use to find the wavelength or frequency of light when the other is known, using the known speed of light.
Worked Example
Finding a light wave's wavelength
Red light has a frequency of 4.5 × 10¹⁴ Hz. Find its wavelength in a vacuum (c = 3 × 10⁸ m/s).
Why Does This Work?
Light, like all electromagnetic waves, obeys the universal wave relationship v = fλ — since c (the speed of light in vacuum) is constant, frequency and wavelength are inversely related: higher frequency light has a shorter wavelength, and vice versa.
Real-Life Example
The delay in seeing distant events
We see the Sun as it was about 8 minutes ago, not as it is right now.
Because light travels at a finite (though extremely fast) speed, and the Sun is about 150 million km away, sunlight takes roughly 8 minutes to reach Earth — a direct, real consequence of light's finite velocity.
Practice
Find the frequency of light with a wavelength of 500 nm (5 × 10⁻⁷ m) in a vacuum (c = 3 × 10⁸ m/s).
MediumCommon mistake
Assuming light travels at the same speed in every material — light's speed of 3 × 10⁸ m/s applies specifically to a VACUUM; it travels more slowly in any medium (glass, water, air), which is the basis of refraction, covered next.
Quick Review
- Speed of light in vacuum, c ≈ 3 × 10⁸ m/s.
- c = fλ relates speed, frequency, and wavelength for light.
- Light travels more slowly in any medium than in a vacuum.