banner

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.

  1. What is the power of one laser pulse?
  2. During the very brief time of the pulse, what is the intensity of the light wave?

The question aims to find the power of one laser pulse and the intensity of the light. Ratio of amount of energy transferred or converted per unit of time is called Power. In the International System of Units, the power unit is the watt, which is equal to one joule per second. In older works, power is also sometimes called activity. Power is a scalar quantity. Power is also related to other quantities as well; for example, the power involved in moving a ground car is the product of the traction force on the wheels and the vehicle’s velocity. Output power of a motor is product of the engine’s torque and the angular velocity of its output shaft. Similarly, the energy dissipated in an electrical element of a circuit is the product of the current flowing through the element and the voltage across that element.

Power is the speed concerning the time in which work is done; it is the time derivative of work:

\[P=\dfrac{dW}{dt}\]

In content of physics, the intensity or flux of radiant energy is the power transferred per unit area, where the area is measured in a plane perpendicular to the energy’s propagation direction. In the SI system, it has units of watts per square meter $(\dfrac{W}{m^{2}})$.

Expert Answer

Part(a)

The power will be the ratio of the energy of emitted over the time during which energy was emitted.

\[P=\dfrac{E}{t}\]

\[P=\dfrac{1.10^{-3}}{1.5.10^{-8}}\]

\[P=66.7kW\]

Part (b)

The intensity is equal to power over the area.

\[I=\dfrac{P}{A}\]

\[I=\dfrac{4P}{\pi d^{2}}=\dfrac{4.66700}{\pi.0.001^{2}}\]

\[I=8.5.10^{10}\dfrac{W}{m^{2}}\]

Numerical Result

The power of one laser pulse is calculated as:

\[P=66.7kW\]

The intensity of the light wave is calculated as:

\[I=8.5.10^{10}\dfrac{W}{m^{2}}\]

Example

LASIK eye surgery uses the pulses of the laser light to shave tissue from the cornea and reshape it. A typical LASIK laser emits a $1.0\:mm$ diameter laser beam with a wavelength of 193 nm. Each laser pulse lasts $20\:ns$ and contains $1.0\: mJ$ of light energy.

– What is the power of one laser pulse?

– During the very brief time of the pulse, what is the intensity of the light wave?

Solution

Part(a)

The power will be the ratio of the energy of emitted over the time during which energy was emitted.

\[P=\dfrac{E}{t}\]

\[P=\dfrac{2.10^{-3}}{2.10^{-8}}\]

\[P=50kW\]

Part (b)

The intensity is equal to power over the area.

\[I=\dfrac{P}{A}\]

\[I=\dfrac{4P}{\pi d^{2}}=\dfrac{4.50000}{\pi.0.001^{2}}\]

\[I=6.366.10^{10}\dfrac{W}{m^{2}}\]

The power of one laser pulse is calculated as:

\[P=50kW\]

The intensity of the light wave is calculated as:

\[I=6.366.10^{10}\dfrac{W}{m^{2}}\]

5/5 - (16 votes)