Convert Wavelength and Frequency
Conversion with the speed of light: f = c/λ and λ = c/f
Wavelength calculator (JavaScript)
Core equation
For electromagnetic waves in vacuum, f = c/λ with c = 299792458 m/s.
Example calculations
Example 1: Frequency from λ = 550 nm
Given: λ = 550 nm = 5.5·10⁻⁷ m
Result: f ≈ 545 THz
Example 2: Wavelength from f = 100 MHz
Given: f = 100 MHz = 1·10⁸ Hz
Result: λ ≈ 3.00 m
Example 3: Microwave range
Given: f = 2.45 GHz
Result: λ ≈ 12.24 cm
Formulas and comprehensive description
Wavelength and frequency are linked by propagation speed. For light in vacuum, the speed is fixed by the physical constant c. Therefore, shorter wavelength always means higher frequency. This conversion is essential in optics, radio engineering, spectroscopy, and communication systems.
Frequency
Wavelength
Speed of light in vacuum
Rule of thumb
Notes for media
Detailed Description
What is Wavelength?
Wavelength (λ) is the spatial distance between two successive identical points of a wave (e.g., between two wave crests or two wave troughs). It is typically measured in meters, but for light waves, it is often specified in nanometers (nm) or micrometers (μm).
For electromagnetic waves such as light, the wavelength is the distance the wave travels during one complete oscillation.
What is Frequency?
Frequency (f) is the number of oscillations or cycles per second. It is measured in Hertz (Hz). A higher frequency means the wave oscillates faster.
- 1 Hz = 1 oscillation per second
- 1 kHz = 1,000 Hz
- 1 MHz = 1,000,000 Hz
- 1 GHz = 1,000,000,000 Hz
- 1 THz = 1,000,000,000,000 Hz
The Relationship Between Wavelength and Frequency
Wavelength and frequency are inversely related. They are connected via the propagation speed:
This gives us the two conversion formulas:
Here, c is the speed of light in vacuum: c ≈ 299,792,458 m/s
Speed of Light in Vacuum
The speed of light in vacuum is a fundamental constant of nature:
- This is the maximum speed at which information can be transmitted
- Light propagates more slowly in materials
- The speed of light is the same for all colors/frequencies in vacuum
The Inverse Relationship: λ ↓ ⇔ f ↑
Most important rule to remember: If wavelength decreases, then frequency increases – and vice versa.
| Wavelength λ | Frequency f | Example |
|---|---|---|
| Small (e.g., 400 nm) | Large (e.g., 750 THz) | Violet light |
| Medium (e.g., 550 nm) | Medium (e.g., 545 THz) | Green light (eye most sensitive) |
| Large (e.g., 700 nm) | Small (e.g., 430 THz) | Red light |
The Electromagnetic Spectrum
Electromagnetic waves differ in their wavelength and frequency. Visible light is only a small part of the entire spectrum:
| Wave Type | Typical Wavelength | Typical Frequency | Application |
|---|---|---|---|
| Radio waves | mm to km | kHz to GHz | Radio, TV, mobile networks |
| Microwaves | mm to cm | GHz | Microwave ovens, WiFi |
| Infrared | 700 nm to 1 mm | MHz to THz | Heat radiation, IR sensors |
| Visible light | 400–700 nm | ~430–750 THz | Human eye |
| Ultraviolet | 10–400 nm | 750 THz to EHz | Disinfection light, medicine |
| X-rays | 0.01–10 nm | EHz | Medical imaging |
| Gamma rays | < 0.01 nm | > EHz | Radioactivity |
Visible Light and Colors
Visible light is a tiny section of the electromagnetic spectrum (approximately 400–700 nm). Different wavelengths are perceived by the human eye as different colors:
| Color | Wavelength (nm) | Frequency (THz) |
|---|---|---|
| Red | 620–750 | ~400–485 |
| Orange | 590–620 | ~485–510 |
| Yellow | 570–590 | ~510–525 |
| Green | 495–570 | ~525–606 |
| Blue | 450–495 | ~606–667 |
| Violet | 380–450 | ~667–789 |
Rule: RED = longer wavelength, smaller frequency | VIOLET = shorter wavelength, larger frequency
Wavelength in Different Media
Important: The formula c = λ·f applies only in vacuum. In materials (water, glass, etc.), the propagation speed is smaller:
Here, v is the speed in the respective medium and λ is the wavelength in the medium.
- Important: The frequency remains constant when transitioning to another medium
- However: The wavelength changes (becomes smaller in denser optical media)
- This is the reason for light refraction
Refractive Index and Wavelength
The refractive index n of a material describes how much the light speed changes:
The wavelength in the medium is then:
- Vacuum: n = 1, λ_Medium = λ_0
- Water: n ≈ 1.33, λ_Medium ≈ 0.75 λ_0
- Glass: n ≈ 1.5, λ_Medium ≈ 0.67 λ_0
Practical Examples and Calculations
Example 1: Red Light in Vacuum
Given: Wavelength λ = 650 nm (red light)
Example 2: WiFi Radio Signal (2.4 GHz)
Given: Frequency f = 2.4 GHz = 2.4 × 10⁹ Hz
Example 3: Infrared (Thermal Camera)
Given: Wavelength λ = 10 μm = 10 × 10⁻⁶ m
Frequently Asked Questions
Q: Why are wavelengths in vacuum larger than in materials?
A: Because the speed of light in materials is smaller. Since f = c/λ and v in the material is smaller, λ must also be smaller.
Q: Is there a limit to wavelengths?
A: Not in principle. Radio waves can be kilometers large, while gamma rays are atomic-sized. The measurement range is limited.
Q: Why can we only see light between 400–700 nm?
A: The human eye has evolutionarily adapted to see in this wavelength range because the sun emits significant energy there.
Q: Does color change when light switches media?
A: No, the color (perceived frequency) remains the same. But the wavelength changes. We perceive color based on frequency, not wavelength.
Q: What is a de Broglie wavelength?
A: Matter (electrons, atoms) also has wave properties. The de Broglie wavelength is λ = h/p, where h is Planck's constant and p is momentum.
Summary
Key Takeaways:
- ✓ Wavelength λ: Spatial distance between identical wave points
- ✓ Frequency f: Number of oscillations per second
- ✓ Basic formula: c = λ·f (in vacuum)
- ✓ Inverse relationship: λ ↓ ⇔ f ↑
- ✓ Visible light: 400–700 nm
- ✓ In materials: λ_Material = λ_0 / n (frequency stays constant)
- ✓ Color depends on frequency, not wavelength
- ✓ Speed of light: c ≈ 299,792,458 m/s = 3 × 10⁸ m/s
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