Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

| 55 | Concept Questions A certain type of laser emits light of known frequency. The light, however, occurs as a series of short pulses, each lasting for a time t0. (a) How is the wavelength of the light related to its frequency? (b) How is the length (in meters) of each pulse related to the time t0?
Problem A laser emits a pulse of light that lasts for . The frequency of the light is . (a) How many wavelengths are there in one pulse? (b) The light enters a pool of water. Its frequency remains the same, but the light slows down to a speed of . How many wavelengths are there now in one pulse?

| 56 | Concept Questions (a) Suppose that the magnitude E of the electric field in an electromagnetic wave triples. By what factor does the intensity S of the wave change? (b) The magnitude B of the magnetic field is much smaller than E because, according to Equation 24.3, B = E/c, where c is the speed of light in a vacuum. If B triples, by what factor does the intensity change? Account for your answers.
Problem The magnitude of the electric field of an electromagnetic wave increases from 315 to 945 N/C. (a) Determine the intensities for the two values of the electric field. (b) What is the magnitude of the magnetic field associated with each electric field? (c) Determine the intensity for each value of the magnetic field. Make sure your answers are consistent with your answers to the Concept Questions.

| 57 | Concept Questions Consult Multiple-Concept Example 5 to review the concepts on which this problem depends. A source is radiating light waves uniformly in all directions. At a certain distance r from the source a person measures the average intensity of the waves. (a) Does the average intensity increase, decrease, or remain the same, as r increases? (b) If the magnitude of the electric field is determined from the average intensity, is the electric field the rms value or the peak value? In both cases, justify your answers.
Problem A light bulb emits light uniformly in all directions. The average emitted power is 150.0 W. At a distance of 5.00 m from the bulb, determine (a) the average intensity of the light, (b) the rms value of the electric field, and (c) the peak value of the electric field.

| 58 | Concept Questions An electric charge is placed in a laser beam. Does a stationary charge experience a force due to (a) the electric field and (b) the magnetic field of the electromagnetic wave? Now suppose that the charge is moving perpendicular to the magnetic field of the beam. Does it experience (c) an electric force and (d) a magnetic force? Account for your answers.
Problem A stationary particle of charge is placed in a laser beam whose intensity is . Determine the magnitude of the (a) electric and (b) magnetic forces exerted on the charge. If the charge is moving perpendicular to the magnetic field with a speed of , find the magnitudes of the (c) electric and (d) magnetic forces exerted on it. Verify that your answers are consistent with your answers to the Concept Questions.

| 59 | Concept Questions The drawing shows light incident on a polarizer whose transmission axis is parallel to the z axis. The polarizer is rotated clockwise through an angle between 0 and 90°. While the polarizer is being rotated, does the intensity of the transmitted light increase, decrease, or remain the same if the incident light is (a) unpolarized, (b) polarized parallel to the z axis, and (c) polarized parallel to the y axis? Provide a reason for each of your answers.

Problem The average intensity of the incident light is 7.0 W/m2. Determine the intensity of the transmitted light for each of the six cases shown in the table.

Intensity of Transmitted Light
Incident Light |  |
Unpolarized |  |
Polarized parallel to z axis |  |
Polarized parallel to y axis |  |

Be sure that your answers are consistent with your answers to the Concept Questions.

| 60 | Concept Question The drawing shows three polarizer/analyzer pairs. The incident light on each pair is unpolarized and has the same intensity. Rank the pairs according to the intensity of the transmitted light, largest first. Provide reasons for your answers.

Problem The average intensity of the unpolarized incident beam is 48 W/m2. Find the average intensity of the transmitted beams for each of the three cases shown in the drawing. Be sure your answers are consistent with your answer to the Concept Question.

| 61 | Concept Question The drawing shows three situations A, B, and C in which an observer and a source of electromagnetic waves are moving along the same line. In each case the source emits a wave of the same frequency. The arrows in each situation denote velocity vectors relative to the ground and have the magnitudes indicated, either v or 2v. Rank the frequencies of the observed electromagnetic waves in descending order (largest first) according to magnitude. Explain your reasoning.
Problem Each of the sources in the drawing emits a frequency of , and the speed v is . Calculate the observed frequency in each of the three cases. Verify that your answers are consistent with your answer to the Concept Question.

| 62 | Concept Questions The drawing shows four sheets of polarizing material, each with its transmission axis oriented differently. Light that is polarized in the vertical direction is incident from the left. One of the sheets is to be removed, with the goal of having some light still pass through the remaining three sheets and emerge on the right. (a) There are a number of possibilities for the sheet that is removed. What are they? Account for your answer. (b) Of the possibilities identified in Concept Question (a), which one allows the greatest light intensity to pass through the sheets?
Problem The light incident from the left in the drawing has an average intensity of 27 W/m2. For each of the possibilities identified in Concept Question (a), determine the average intensity of the light that emerges on the right in the drawing. Be sure that your answer is consistent with your answer to Concept Question (b).

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