Review: Calculate the Amplitude of Electric Field Inside a Helium-Neon Laser Beam
A helium-neon laser produces a beam of diameter 1.75 mm, delivering 2.00 × 10^18 photons/s. Each photon has a wavelength of 633 nm. Calculate the amplitudes of the electric fields.
The amplitude of the electric field inside the beam is approximately 3.518 x 10^9 V/m. To calculate the amplitude of the electric field inside the beam, we can use the formula:
E = √(2 × P / (c × ε₀ × A))
Calculation of Electric Field Amplitude
E = √(2 × P / (c × ε₀ × A))
where:
E is the amplitude of the electric field,
P is the power of the beam in watts,
c is the speed of light in meters per second,
ε₀ is the vacuum permittivity (8.854 x 10^-12 F/m),
A is the cross-sectional area of the beam in square meters.
Calculation Steps:
1. Calculate the power of the beam using the given information.
- Number of photons emitted per second: 2.00 × 10^18 photons/s - Energy of each photon using Planck's equation: E = hc / λ - Power: P = E × N = 9.0875 J/s
2. Calculate the cross-sectional area of the beam.
- Diameter: 1.75 mm = 1.75 x 10^-3 m - Radius: 8.75 x 10^-4 m - Area: A = π × r² = 2.394 x 10^-6 m²
3. Substitute the values into the formula for the electric field.
- Calculated amplitude of electric field: 3.518 x 10^9 V/m
Therefore, the amplitude of the electric field inside the helium-neon laser beam is approximately 3.518 x 10^9 V/m.