In LASIK surgery, a laser is used to reshape the cornea of the eye to improve vision. The laser produces extremely short pulses of light, each containing $1.0mJ$of energy.

a. There are $9.7\times {10}^{14}$photons in each pulse. What is the wavelength of the laser?

b. Each pulse lasts a mere $20ns$. What is the average power delivered to the cornea during a pulse?

We have given that,

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

we have to find the wavelength of laser.

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

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

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

$\Rightarrow \lambda =\left(\frac{9.7\times {10}^{14}}{1.0\times {10}^{-3}J}\right)\left(6.626\times {10}^{-34}J.s\right)\left(3.0\times {10}^{8}m/s\right)$

$\Rightarrow \lambda =193nm$

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 $\overline{P}=\frac{E_{pulse}}{∆t_{pulse}}$

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

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