/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 71 An unpolarized beam of light (in... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 22: Problem 71

An unpolarized beam of light (intensity \(I_{0}\) ) is moving in the \(x\) -direction. The light passes through three ideal polarizers whose transmission axes are (in order) at angles \(0.0^{\circ}, 45.0^{\circ},\) and \(30.0^{\circ}\) counterclockwise from the \(y\) -axis in the \(y z\) -plane. (a) What is the intensity and polarization of the light that is transmitted by the last polarizer? (b) If the polarizer in the middle is removed, what is the intensity and polarization of the light transmitted by the last polarizer?

Short Answer

Expert verified
Answer: a) With three polarizers: The final intensity is \(I_3 = I_2 \cdot \cos^{2}(30^{\circ})\) and the polarization angle is \(30^{\circ}\) to the y-axis. b) With only the first and third polarizers: The final intensity is \(I_3 = I_1 \cdot \cos^{2}(30^{\circ})\) and the polarization angle is also \(30^{\circ}\) to the y-axis.

Step by step solution

01

Intensity and polarization after first polarizer

Since the first polarizer has a transmission axis at \(0.0^{\circ}\), the light passing through it will become linearly polarized parallel to the y-axis. As it is an ideal polarizer, the intensity of the light remains the same. So, the intensity of light after passing through the first polarizer is \(I_{1} = I_{0}\). #Step 2: Light passing through the second polarizer#
02

Intensity and polarization after second polarizer

The angle between the transmission axis of the first and second polarizers is \(45.0^{\circ}\). Using Malus' law, the intensity of light after passing through the second polarizer is \(I_{2} = I_{1} \cdot \cos^{2}(45^{\circ})\). As the second polarizer is at \(45^{\circ}\) counterclockwise from the y-axis, the transmitted light will be linearly polarized with a polarization angle of \(45^{\circ}\) to the y-axis. #Step 3: Light passing through the third polarizer#
03

Intensity and polarization after the third polarizer

The angle between the transmission axis of the second and third polarizers is \(30.0^{\circ}\). Using Malus' law again, the intensity of light after passing through the third polarizer is \(I_{3} = I_{2} \cdot \cos^{2}(30^{\circ})\). The transmitted light is now linearly polarized with a polarization angle of \(30^{\circ}\) to the y-axis. #b) Case with only the first and third polarizers# #Step 4: Light passing through the first polarizer#
04

Intensity and polarization after first polarizer (removing the middle polarizer)

Same as before, the first polarizer polarizes the light parallel to the y-axis and does not change the intensity \(I_{1} = I_{0}\). #Step 5: Light passing through the third polarizer#
05

Intensity and polarization after the third polarizer (removing the middle polarizer)

Since there is no middle polarizer, the angle between the first and third polarizers' transmission axes is \(30.0^{\circ}\). Using Malus' law, the intensity of light after passing through the third polarizer is \(I_{3} = I_{1} \cdot \cos^{2}(30^{\circ})\). Again, the transmitted light is linearly polarized with a polarization angle of \(30^{\circ}\) to the y-axis.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The solar panels on the roof of a house measure \(4.0 \mathrm{m}\) by $6.0 \mathrm{m} .\( Assume they convert \)12 \%$ of the incident EM wave's energy to electric energy. (a) What average power do the panels supply when the incident intensity is \(1.0 \mathrm{kW} / \mathrm{m}^{2}\) and the panels are perpendicular to the incident light? (b) What average power do the panels supply when the incident intensity is \(0.80 \mathrm{kW} / \mathrm{m}^{2}\) and the light is incident at an angle of \(60.0^{\circ}\) from the normal? (W) tutorial: solar collector) (c) Take the average daytime power requirement of a house to be about 2 kW. How do your answers to (a) and (b) compare? What are the implications for the use of solar panels?
An electric dipole antenna used to transmit radio waves is oriented vertically.At a point due north of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?
Just after sunrise, you look straight up at the sky. Is the light you see polarized? If so, in what direction?

You and a friend are sitting in the outfield bleachers of a major league baseball park, 140 m from home plate on a day when the temperature is \(20^{\circ} \mathrm{C}\). Your friend is listening to the radio commentary with headphones while watching. The broadcast network has a microphone located \(17 \mathrm{m}\) from home plate to pick up the sound as the bat hits the ball. This sound is transferred as an EM wave a distance of \(75,000 \mathrm{km}\) by satellite from the ball park to the radio. (a) When the batter hits a hard line drive, who will hear the "crack" of the bat first, you or your friend, and what is the shortest time interval between the bat hitting the ball and one of you hearing the sound? (b) How much later does the other person hear the sound?
The magnetic field of an EM wave is given by \(B_{y}=\) $B_{\mathrm{m}} \sin (k z+\omega t), B_{x}=0,\( and \)B_{z}=0 .$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the electric field of this wave.
See all solutions

Recommended explanations on Physics Textbooks

Astrophysics

Read Explanation

Energy Physics

Read Explanation

Dynamics

Read Explanation

Translational Dynamics

Read Explanation

Famous Physicists

Read Explanation

Kinematics Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.