Question

A laser had a power output of 2mW and a beam diameter of 2mm. (A) what is the amplitude of the electric field in the electromagnetic waves emitted by this device? Find (b) the total energy in a 2 meter length of the laser beam and (c) the momentum transferred to a perfect mirror by this laser beam. (D) the index of refraction of water is about 1.33. What is the wavelength in water of a light wave whose wavelength in air is 600 mm.

Answer 1

Given,
Power of Beam = 2 * 10^-3 W
Radius of Beam = 2/2 * 10^-3 m = 1 * 10^-3 m
µ₀ = 4π×10⁻⁷ H

a)
Intensity of laser S = Power of Beam / Area
S = 2 * 10^-3 W / (3.14 * (1 * 10^-3)^2)
S = 636.94 W/m^2

Intensity of Electromagnetic wave S = Em^2 / 2*uo*c
Substituing Value
636.94 = Em^2 / 2 * 4π×10⁻⁷ * 3* 10^8
Em = sqrt(636.94 * 753.6)
Em = 692.8

b)
   time = distance / Speed
   time = 2 m /3 *10^8 m/s
time = 0.667 * 10^-8 Sec

Total Energy =  power * time
Total Energy = 2 * 10^-3 W * 0.667 * 10^-8
Total Energy = 1.33 * 10^-11 J

c) pressure in an electromagnetic wave is given by - 1/2 * Energy Density

where,
Energy Density = Energy / Volume
Energy Density = 4.25 * 10^-6 J/m^3

Pressure = 4.25 * 10^-6
Pressure = 4.24 * 10^-6 N/m^2

Momentum Transferred = Pressure * area
Momentum Transferred = 4.24 * 10^-6 * 3.14 * (1 * 10^-3)^2
Momentum Transferred = 13.30 * 10^-12 N