Question

What are the frequency and wavelength ranges of visible light?

Short answer

Wavelength: 380-700 nm. Frequency: 4.3 to 7.9 \( \times 10^{14} \) Hz.

Step-by-step solution

Understanding Visible Light

Visible light is the portion of the electromagnetic spectrum that is visible to the human eye. It ranges from violet to red in color.

Identify Wavelength Range

Visible light has wavelengths ranging approximately from 380 nanometers (nm) for violet light to 700 nanometers (nm) for red light.

Calculate Frequency Range

Use the formula for the speed of light: \[ c = u \times \lambda \], where \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) meters per second), \( u \) is the frequency, and \( \lambda \) is the wavelength. Rearrage to find frequency: \[ u = \frac{c}{\lambda} \]. For \( \lambda = 700 \) nm, \( u \approx \frac{3 \times 10^8}{700 \times 10^{-9}} = 4.3 \times 10^{14} \) Hz. For \( \lambda = 380 \) nm, \( u \approx \frac{3 \times 10^8}{380 \times 10^{-9}} = 7.9 \times 10^{14} \) Hz.

Summarize Ranges

Thus, the wavelength range of visible light is from 380 nm to 700 nm, and the frequency range is from 4.3 \( \times 10^{14} \) Hz to 7.9 \( \times 10^{14} \) Hz.

Key concepts

wavelength of visible light

Visible light is the part of the electromagnetic spectrum that humans can see. Its wavelength defines the color that we perceive. Wavelengths of visible light range from 380 nanometers (nm) to 700 nanometers (nm).
The shorter wavelengths (~380 nm) are associated with violet and blue light. Longer wavelengths (~700 nm) correspond to red light.

• Violet: ~380-450 nm
• Blue: ~450-495 nm
• Green: ~495-570 nm
• Yellow: ~570-590 nm
• Orange: ~590-620 nm
• Red: ~620-700 nm

Understanding these ranges is essential because different wavelengths have different properties and uses in various scientific and practical applications.

frequency of visible light

Frequency describes the number of wave cycles that pass a point per second and is measured in Hertz (Hz). The frequency of visible light corresponds to its wavelength. Since the speed of light, \c\, is constant at approximately \3 \times 10^8\text{ m/s}\, you can calculate frequency using the formula: \[ u = \frac{c}{\textcolor{blue}{\right.\textcolor{black}{\textcolor{blue}{(λ)\right.}}} \].
Thus, for different wavelengths within the visible spectrum:

• For violet light (380 nm):
  Frequency ≈ \[ \frac{3 \times 10^8}{380 \times 10^{-9}} \approx 7.9 \times 10^{14}\ Hz \]
• For red light (700 nm):
  Frequency ≈ \[ \frac{3 \times 10^8}{700 \times 10^{-9}} \approx 4.3 \times 10^{14}\ Hz \]

Knowing the frequency range helps in fields like telecommunications, where specific frequencies are critical for signal transmission.

electromagnetic spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation, from gamma rays to radio waves. Each type of radiation is distinguished by its wavelength and frequency.
Visible light represents only a small portion of this spectrum, ranging from 380 nm to 700 nm in wavelength. Outside this range, you find:

• Ultraviolet (UV) light: Wavelengths shorter than 380 nm,
  more energetic than visible light.
• Infrared (IR) light: Wavelengths longer than 700 nm,
  felt as heat.

The electromagnetic spectrum is essential for many technologies,
including medical imaging, communication systems,
and even cooking (microwaves).
Understanding where visible light fits into this spectrum
helps appreciate its unique properties and applications.