Question

The light from a red laser pointer has a wavelength of about 600 nm. If this laser has a power of 0.18 mW, what is the momentum carried by a 1.8-s pulse of this radiation? (in kg · m/s)

The magnetic field associated with an electromagnetic wave has an amplitude of 1.6 μT.

(a) What is the amplitude of the electric field associated with this wave? (in V/m)

(b) What is the intensity of this wave? (W/m²⁾

(c) What is the radiation pressure associated with this wave? (N/m²⁾

(d) How much momentum is carried by a 1.3-s pulse of this wave over an area of 16 m²? (kg · m/s)

Answer 1

We know that, E = p c

where, c = speed of light = 3 x 10⁸ m/s

(0.18 x 10^-3 J/s) (1.8 s) = p (3 x 10⁸ m/s)

p = (0.324 x 10^-3 J) / (3 x 10⁸ m/s)

p = 0.108 x 10^-11 kg.m/s

p = 1.08 x 10^-12 kg.m/s

(a) What is the amplitude of the electric field associated with this wave?

using a formula, we have

E₀ = c B₀ (3 x 10⁸ m/s) (1.6 x 10^-6 T)

E₀ = 4.8 x 10² V/m

E₀ = 480 V/m

(b) What is the intensity of this wave?

using a formula, we have

I = (c ₀ E²) / 2

I = [(3 x 10⁸ m/s) (8.85 x 10^-12 C²/Nm²) (480 V/m)²] / 2

I = 305.8 W/m²

(c) What is the radiation pressure associated with this wave?

using a formula, we have

P_rad = I / c = (305.8 W/m²) / (3 x 10⁸ m/s)

P_rad = 101.9 x 10^-8 N/m²

P_rad = 1.02 x 10^-6 N/m²

(d) How much momentum is carried by a 1.3-s pulse of this wave over an area of 16 m²?

using a formula, we have

p = P_rad A t = (1.02 x 10^-6 N/m²) (16 m²) (1.3 sec)

p = 2.12 x 10^-5 kg.m/s