Calculating the Amplitudes of Electric and Magnetic Fields in a Helium-Neon Laser

Question:

What are the amplitudes of the oscillating electric and magnetic fields in a typical helium-neon laser emitting 633-nm-wavelength light?

Answer:

The amplitudes of the oscillating electric and magnetic fields in the laser beam are determined by the power of the laser, the diameter of the beam, and the intensity of the light. In this case, the helium-neon laser emits 633-nm-wavelength light in a 1.5-mm-diameter beam with a power of 1.3 mW.

Calculations for Electric and Magnetic Field Amplitudes:

Area of the Beam:

The area of the beam is calculated using the formula A = πd²/4, where d is the diameter of the beam. Substituting the values, we get:

A = π * (1.5 x 10⁻³)² / 4 = 1.77 x 10⁻⁶ m²

Intensity of the Beam:

The intensity of the beam is calculated as I = P / A, where P is the power of the laser. Substituting the values, we get:

I = (1.3 x 10⁻³ W) / (1.77 x 10⁻⁶ m²) = 734.5 W/m²

Amplitude of the Electric Field:

The amplitude of the electric field (E₀) is calculated using the formula E₀ = sqrt(2I / ε₀c), where ε₀ is the vacuum permittivity and c is the speed of light. Substituting the values, we get:

E₀ = 743.8 N/C

Amplitude of the Magnetic Field:

The amplitude of the magnetic field (B₀) is calculated using the formula B₀ = sqrt(2μ₀I / c), where μ₀ is the vacuum permeability. Substituting the values, we get:

B₀ = 2.48 x 10⁻⁶ T

Therefore, the amplitude of the oscillating electric field is 743.8 N/C and the amplitude of the oscillating magnetic field is 2.48 x 10⁻⁶ T.