recall that wavelengths in the range 400–700 nm in free space are visible to the human eye

Electromagnetic Spectrum

The electromagnetic (EM) spectrum comprises all possible wavelengths (or frequencies) of electromagnetic radiation, ranging from very long radio waves to extremely short gamma rays. Each region of the spectrum has characteristic sources, interactions with matter, and practical uses.

Key Regions of the Spectrum

Region	Wavelength (nm)	Frequency (THz)	Typical Sources
Radio	≥ 10⁶	≤ 0.3	Transmitters, antennas
Microwave	10³ – 10⁶	0.3 – 300	Radar, satellite communication
Infrared	700 – 10⁶	300 – 430	Thermal emitters, remote controls
Visible	400 – 700	430 – 750	Sunlight, LEDs, lasers
Ultraviolet	10 – 400	750 – 30 000	Sun, U \cdot lamps
X‑ray	0.01 – 10	30 000 – 30 000 000	Medical imaging, astronomical sources
Gamma ray	< 0.01	> 30 000 000	Radioactive decay, nuclear reactions

Visible Light: 400–700 nm

The human eye can detect electromagnetic radiation only within a narrow band of wavelengths, approximately 400 nm (violet) to 700 nm (red). Light outside this range is invisible to us, though it can still affect the eye (e.g., ultraviolet can cause sunburn).

When light of a particular wavelength enters the eye, it is focused onto the retina where photoreceptor cells (cones) respond. The three types of cone cells are most sensitive to:

• Short‑wavelength (S) – peak near 420 nm (blue)
• Medium‑wavelength (M) – peak near 534 nm (green)
• Long‑wavelength (L) – peak near 564 nm (red)

Our perception of colour arises from the relative stimulation of these three cone types.

Relationship Between Wavelength, Frequency, and Speed

All electromagnetic waves travel at the speed of light in vacuum, denoted $c$, where

$$c = \lambda \, f$$

Here $c = 3.00 \times 10^{8}\ \text{m s}^{-1}$, $\lambda$ is the wavelength, and $f$ is the frequency. For visible light, substituting $\lambda = 400\ \text{nm}$ gives $f \approx 7.5 \times 10^{14}\ \text{Hz}$, and $\lambda = 700\ \text{nm}$ gives $f \approx 4.3 \times 10^{14}\ \text{Hz}$.

Why the 400–700 nm Range?

The limits of human vision are determined by the absorption spectra of the photopigments in the cone cells. Photons with energies lower than those corresponding to 700 nm (red) do not have enough energy to trigger a photochemical response, while photons with energies higher than those corresponding to 400 nm (violet) are absorbed by ocular media before reaching the retina.

Practical Implications

1. Design of lighting: LEDs and lamps are engineered to emit within the visible band for efficient illumination.
2. Colour measurement: Spectrophotometers use the 400–700 nm range to quantify colour of objects.
3. Safety: Protective eyewear must block ultraviolet (< 400 nm) and infrared (> 700 nm) radiation that can damage the eye.

Summary

• The electromagnetic spectrum covers all wavelengths from > 10⁶ nm (radio) to < 0.01 nm (gamma).
• Human vision is limited to the visible region, 400–700 nm, corresponding to frequencies 430–750 THz.
• The speed‑of‑light relation $c = \lambda f$ links wavelength and frequency for all EM radiation.
• Understanding the visible range is essential for applications in lighting, imaging, and eye safety.