Answer :
The wavelength of the laser is 19.4 nm and the average power delivered to the eye during a pulse is 50000 W.
(a) The energy of a laser pulse in terms of number of photons is =
= E = N X (hc / λ)
Where,
λ = wavelength
N = Number of photons in each laser pulse
h = Planck constant
c = Speed of light
We need to find the wavelength, then re-arrange the equation
= λ = N X (hc / E)
Converting the unit the energy from J to eV, we have,
= E = 1 X 10⁻³ [ 1 eV / 1.6 X 10⁻¹⁹ ]
= E = 6.25 X 10¹⁵ eV
Replacing,
= λ = N X (hc / E)
= λ = [ ( 9.7 X 10¹⁴ X 4.136 X 10⁻¹⁵ X 3 X 10⁸ ) / 6.25 X 10¹⁵ ]
= λ = 19.4 nm
(b) Energy = E = 1 mJ
Time = t = 20 ns
Thus, average power = p =
= p = E/t
= p = 1 X 10⁻³ / 20 X 10⁻⁹
= p = 0.05 X 10⁶
= p = 50000 W
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