Question

LASIK eye surgery uses pulses of laser light to shave off tissue

from the cornea, reshaping it. A typical LASIK laser emits a

1.0-mm-diameter laser beam with a wavelength of 193 nm. Each

laser pulse lasts 15 ns and contains 1.0 mJ of light energy.

a. What is the power of one laser pulse?

b. During the very brief time of the pulse, what is the intensity

of the light wave?

Short answer

a. The power of one laser pulse is$6.67\times {10}^{4}W.$

b. During the very brief time of the pulse, the intensity

of the light wave is$8.5\times {10}^{10}W/m^2$.

Step-by-step solution

Part a Step 1: Given data

The energy of laser pulse $U=1mJ=1\times {10}^{-3}J$

The laser pulse lasts for a time period of $t=15ns=\left(15\times {10}^{-9}\right)s$

Diameter of laser beam,role="math" localid="1649825424330" $d=1mm$

Determination of power

The power of laser beam can be determined by,

$$\begin{gathered} P=\frac{U}{t} \\ P=\frac{1\times {10}^{-4}J}{15\times {10}^{-9}s} \\ P=6.67\times {10}^{4}W \end{gathered}$$

Part b Step 1: Given data

Diameter of laser beam, $d=1mm$

Therefore, the radius of the laser beam is,

$$\begin{gathered} r=\frac{1}{2}mm \\ r=0.5mm \\ r=5\times {10}^{-4}m \end{gathered}$$

During a very short time of the pulse, the intensity

of the light wave can be determined by, $I=\frac{P}{A}$, where $A$is the cross-sectional area of the light beam.

Therefore, the intensity,

role="math" localid="1649826456280" $$\begin{gathered} I=\frac{P}{A} \\ I=\frac{6.67\times {10}^{4}W}{\pi {\left(5\times {10}^{-4}m\right)}^2} \\ I=8.5\times {10}^{10}W/m^2 \end{gathered}$$