Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to ignite nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of 2.09\times 10^{11}~\text{V/m}2.09×10 11 V/m for a time of 1.00 ns. What energy does it deliver on a 1.00~\mathrm{mm^2}1.00 mm 2 area?

The energy it delivers is 5.799x10⁴J

Explanation:

Given data:

Em = maximum electric field = 2.09x10¹¹V/m

t = time = 1 ns = 1x10⁻⁹s

A = area = 1 mm² = 1x10⁻⁶m²

Question: What energy does it deliver, E = ?

First, you need to calculate the intensity of the wave:

Here

c = speed of light = 3x10⁸m/s

ε = permittivity = 8.85x10⁻¹²C²/N m²

Substituting:

The energy:

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.