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Chapter 33: Problem 22

A black, totally absorbing piece of cardboard of area \(A=2.0 \mathrm{~cm}^{2}\) intercepts light with an intensity of \(10 \mathrm{~W} / \mathrm{m}^{2}\) from a camera strobe light. What radiation pressure is produced on the cardboard by the light?

Short Answer

Expert verified
The radiation pressure on the cardboard is approximately \(3.33 \times 10^{-8} \text{ Pa}\).

Step by step solution

01

Understand the concept of radiation pressure

Radiation pressure is the pressure exerted by electromagnetic radiation on a surface. When the surface absorbs the light entirely, as in this problem, the radiation pressure can be calculated using the formula: \[ P = \frac{I}{c} \] where \(I\) is the intensity of the light and \(c\) is the speed of light in a vacuum, approximately \(3 \times 10^8 \text{ m/s} \).
02

Convert area units if necessary

Ensure that all units are consistent. The area is given in \(\text{cm}^2\), but this area is not directly needed for calculating radiation pressure as only intensity is required. Hence, no conversion is necessary.
03

Use the correct formula for totally absorbing surface

For a totally absorbing surface, the radiation pressure \(P\) is given by \( P = \frac{I}{c} \). Substituting the given intensity value \(I = 10 \text{ W/m}^2\) and speed of light \(c = 3 \times 10^8 \text{ m/s}\), we can find \(P\).
04

Calculate the radiation pressure

Calculate the radiation pressure using the formula: \[ P = \frac{10 \text{ W/m}^2}{3 \times 10^8 \text{ m/s}} \] Performing the division, \[ P \approx 3.33 \times 10^{-8} \text{ N/m}^2 \] or \(\text{Pascals (Pa)}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Intensity of Light
The intensity of light is the amount of energy that light waves carry per unit area per unit time. It tells us how strong or weak the light is at a given distance. Imagine light as rain falling on a field. The intensity of light is like the thickness of the rain; a higher intensity means a heavier downpour. What affects light intensity?
  • The power of the light source: Stronger light bulbs or lasers produce more intense light.
  • Distance from the source: The farther from the light source, the less intense the light becomes.
In the context of our exercise, the intensity given is a measure of how much light energy the camera strobe sends towards the cardboard. The intensity is used in our calculations to determine the pressure the light exerts.
Electromagnetic Radiation
Electromagnetic radiation includes all types of light waves, not just the visible spectrum. It's a form of energy that travels through space at the speed of light. Characteristics of electromagnetic radiation:
  • Wavelength: distance between two peaks of the wave.
  • Frequency: how many waves pass a point in one second.
  • Speed: How fast light travels, which is constant in a vacuum.
In our problem, the cardboard absorbs this electromagnetic radiation entirely. When absorbed, it leads to what we calculate as radiation pressure.
Speed of Light
The speed of light is one of the most crucial constants in physics, commonly denoted as "c." It represents how fast electromagnetic waves, like light, travel in a vacuum.Key facts about the speed of light:
  • It is approximately \(3 \times 10^8 \text{ m/s} \).
  • This speed is considered an upper limit for how fast information can travel.
  • The constancy of light's speed is essential for understanding many physics phenomena, including relativity.
In the exercise, the speed of light is used to calculate radiation pressure since it determines how quickly the light hits and affects the cardboard.

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Most popular questions from this chapter

The index of refraction of benzene is \(1.8\). What is the critical angle for a light ray traveling in benzene toward a flat layer of air above the benzene?

A small spaceship with a mass of only \(1.5 \times 10^{3} \mathrm{~kg}\) (including an astronaut) is drifting in outer space with negligible gravitational forces acting on it. If the astronaut turns on a \(10 \mathrm{~kW}\) laser beam, what speed will the ship attain in \(1.0\) day because of the momentum carried away by the beam?

Light that is traveling in water (with an index of refraction of \(1.33\) ) is incident on a plate of glass (with index of refraction 1.53). At what angle of incidence does the reflected light end up fully polarized?

The maximum electric field \(10 \mathrm{~m}\) from an isotropic point source of light is \(2.0 \mathrm{~V} / \mathrm{m}\). What are (a) the maximum value of the magnetic field and (b) the average intensity of the light there? (c) What is the power of the source?

Frank D. Drake, an investigator in the SETI (Search for Extra-Terrestrial Intelligence) program, once said that the large radio telescope in Arecibo, Puerto Rico (Fig. 33-36), "can detect a signal which lays down on the entire surface of the earth a power of only one picowatt." (a) What is the power that would be received by the Arecibo antenna for such a signal? The antenna diameter is \(300 \mathrm{~m}\). (b) What would be the power of an isotropic source at the center of our galaxy that could provide such a signal? The galactic center is \(2.2 \times 10^{4}\) ly away. A light-year is the distance light travels in one year.
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