Ch 16: Traveling Waves

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 16: Traveling Waves

Problem 68b

Chapter 16, Problem 68b

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

Verified step by step guidance

Step 1: Recall the formula for intensity, which is the power per unit area: \( I = \frac{P}{A} \). Here, \( I \) is the intensity, \( P \) is the power, and \( A \) is the area over which the power is distributed.

Step 2: Calculate the power \( P \) of the laser pulse. Power is the energy delivered per unit time, so \( P = \frac{E}{t} \), where \( E \) is the energy of the pulse (1.0 mJ = 1.0 \( \times \) 10\(^{-3}\) J) and \( t \) is the duration of the pulse (15 ns = 15 \( \times \) 10\(^{-9}\) s).

Step 3: Determine the area \( A \) of the laser beam. The beam is circular with a diameter of 1.0 mm (radius = 0.5 mm = 0.5 \( \times \) 10\(^{-3}\) m). The area of a circle is given by \( A = \pi r^2 \).

Step 4: Substitute the values of \( P \) and \( A \) into the intensity formula \( I = \frac{P}{A} \) to calculate the intensity of the light wave.

Step 5: Ensure that all units are consistent (e.g., energy in joules, time in seconds, area in square meters) before performing the calculations. This will yield the intensity in units of watts per square meter (W/m\(^2\)).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Intensity of Light

Intensity is defined as the power per unit area carried by a wave. In the context of light, it quantifies how much energy is transmitted through a specific area in a given time. The formula for intensity (I) is I = P/A, where P is the power and A is the area. Understanding intensity is crucial for analyzing how concentrated the energy from the laser beam is during the pulse.

Power of the Laser Pulse

Power is the rate at which energy is transferred or converted. For the laser pulse in LASIK surgery, the power can be calculated by dividing the energy contained in the pulse by the duration of the pulse. In this case, with 1.0 mJ of energy over 15 ns, the power can be determined, which is essential for calculating the intensity of the light wave.

Area of the Laser Beam

The area over which the laser beam is focused is critical for determining intensity. The area of a circular beam can be calculated using the formula A = πr², where r is the radius of the beam. Given that the diameter of the laser beam is 1.0 mm, this area will be used in conjunction with the power to find the intensity of the light wave during the pulse.

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