Pulsed dye lasers emit light of wavelength 585 nm in 0.45 ms pulses to remove skin blemishes such as birthmarks. the beam is usually focused onto a circular spot 3.4 mm in diameter. suppose that the output of one such laser is 20.0 w .(a) what is the energy of each photon, in ev? (b) how many photons per square millimeter are delivered to the blemish during each pulse?

a) E₀ = 2.125 eV, b)     # photon2 = 9.2 10¹⁵ photons / mm²

Explanation:

a) To calculate the energy of a photon we use Planck's education

      E = h f

And the ratio of the speed of light

     c = λ f

We replace

      E = h c /λ

Let's calculate

      E₀ = 6.63 10⁻³⁴ 3 10⁸/585 10⁻⁹

      E₀ = 3.40 10⁻¹⁹ J

Let's reduce

     E₀ = 3.4 10⁻¹⁹ J (1 eV / 1.6 10⁻¹⁹ J)

     E₀ = 2.125 eV

b) Let's look for the energy in each pulse

       P = E / t

       E = P t

       E = 20.0 0.45 10⁻³

       E = 9 10⁻³ J

let's use a ratio of proportions (rule of three) if we have the energy of a photon (E₀), to have the energy of 9 10⁻³ J

       # photon = 9 10⁻³ /3.40 10⁻¹⁹

      # photon = 2.65 10¹⁶ photons

Let's calculate the areas

Focus area

      A₁ = π r²

     A₁ = π (3.4/2)²

     A₁ = 9,079 mm²2

Area requested for calculation r = 1 mm

     A₂ = π 1²

     A₂ = 3.1459 mm²

Let's use another rule of three. If we have 2.65 106 photons in an area A1 how many photons in an area A2

    # photon2 = 2.65 10¹⁶ 3.1459 / 9.079

   # photon2 = 9.2 10¹⁵ photons / mm²

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.