91Ó°ÊÓ

We have given that,

The laser contain $1.0mJ$of energy in extremely short pulses of light and there are $9.7×{10}^{14}$photons in each pulse.

we have to find the wavelength of laser.

The energy of each photon is $E_{photon}=hf=\frac{hc}{\mathrm{λ}}.$

A pulse contains $9.7×{10}^{14}$photons so the total energy in the pulse is $(9.7×{10}^{14})E_{photon}=1.0×{10}^{-3}J.$

Thus, the wavelength is$(9.7×{10}^{14})\frac{hc}{\mathrm{λ}}=1.0×{10}^{-3}J$

$⇒\mathrm{λ}=\left(\frac{9.7×{10}^{14}}{1.0×{10}^{-3}J}\right)\left(6.626×{10}^{-34}J.s\right)\left(3.0×{10}^{8}m/s\right)$

$⇒\mathrm{λ}=193nm$

The wavelength of laser is$193nm.$

We have given that,

The laser contain $1.0mJ$of energy in extremely short pulses of light and each pulse lasts a mere $20ns.$

We have to find the average power delivered to cornea during a pulse.

The average power per pulse is $\stackrel{¯}{P}=\frac{E_{pulse}}{∆t_{pulse}}$

$\stackrel{¯}{P}=\frac{E_{pulse}}{∆t_{pulse}}=\frac{1.0×{10}^{-3}J}{20×{10}^{-9}s}=50kW$

The average power delivered to the cornea during a pulse$50kW.$