/*! 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 47 When unpolarized light is incide... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 24: Problem 47

When unpolarized light is incident on a polarizer-analyzer pair, \(30 \%\) of the original light intensity passes the analyzer. What is the angle between the transmission axes of the polarizer and analyzer?

Short Answer

Expert verified
The angle between the transmission axes is approximately \(39.23^\circ\).

Step by step solution

01

Understand Malus's Law

Malus's Law states that the intensity of polarized light after passing through a polarizer, or analyzer, is given by \( I = I_0 \cos^2\theta \), where \( I \) is the intensity after the analyzer, \( I_0 \) is the initial intensity (intensity after the polarizer), and \( \theta \) is the angle between the transmission axes of the polarizer and analyzer.
02

Define the Initial Conditions

For unpolarized light passing through a polarizer, the intensity becomes half the original intensity due to the polarizer's action. Therefore, if we start with an intensity \( I_0' \), the intensity after the polarizer \( I_0 \) is \( \frac{1}{2}I_0' \). The intensity after the analyzer is given as \( 30\% \) of the original intensity \( I_0' \), which is \( 0.3 I_0' \).
03

Apply Malus's Law to the System

Using Malus's Law, the intensity after the analyzer is \( I = I_0 \cos^2\theta \). Plugging in the known values, \( 0.3 I_0' = \frac{1}{2} I_0' \cos^2\theta \). Simplifying the equation gives \( \cos^2\theta = \frac{0.3}{0.5} = 0.6 \).
04

Solve for \( \theta \)

Take the square root of both sides to find \( \cos\theta \), which gives \( \cos\theta = \sqrt{0.6} \). To determine \( \theta \), take the arccosine: \( \theta = \cos^{-1}(\sqrt{0.6}) \). This results in \( \theta \approx 39.23^\circ \).

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!

Key Concepts

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

Malus's Law
Malus's Law is a fundamental principle in optics, specifically dealing with the behavior of polarized light. It describes how the intensity of light changes as it passes through a polarizer-analyzer pair.
This law is mathematically expressed as:
  • \( I = I_0 \cos^2 \theta \)
  • Where:
    • \( I \) represents the intensity of light after passing through the analyzer,
    • \( I_0 \) is the intensity of light after the polarizer,
    • and \( \theta \) is the angle between the transmission axes of the polarizer and the analyzer.
Malus's Law is crucial for understanding how the direction relative to the polarization affects the resulting intensity.
The law shows that if the transmission axes are perpendicular, no light passes, and as they align, maximum light transmission can be achieved.
Unpolarized Light
Unpolarized light is light that vibrates in multiple planes. Most common sources of light, such as sunlight and light bulbs, emit unpolarized light.
In unpolarized light, the electric field vectors are distributed evenly across all possible directions perpendicular to the direction of the light wave.
  • When unpolarized light is passed through a polarizer, it becomes polarized. This means its electric field vibrates in only one plane.
  • After passing through the first polarizer, the intensity of this light is reduced by half. This is because any polarization direction is equally probable.
The conversion of unpolarized light to polarized light is a key step in applying Malus's Law to determine subsequent light behavior.
Understanding this enables us to determine how much light intensity will be reduced after passing through a polarizer and further analyzed by an analyzer.
Polarizer-Analyzer Pair
The polarizer-analyzer pair is an arrangement used to study and manipulate light polarization.
This setup consists of two optical devices:
  • Polarizer: Acts as the first filter the light encounters. It only allows light vibrating in a specific direction to pass through. The result is polarized light with intensity reduced to half of that of the unpolarized source.
  • Analyzer: The second optical device that the polarized light passes through. It further filters the light based on the angle \( \theta \) relative to the polarizer's axis, as described by Malus's Law.
Together, these devices are crucial for experiments and applications involving light polarization.
The alignment or misalignment of their transmission axes directly affects the resulting light intensity, which can be calculated using Malus's Law.
This setup is widely used in scientific research and various technologies such as polarized sunglasses and optical instruments.
Light Intensity
Light intensity refers to the amount of energy that light waves deliver per unit area. In the context of polarization, it changes as light passes through polarizers and analyzers.
Key points about light intensity in this context:
  • When unpolarized light first encounters a polarizer, its intensity is reduced by half. This is because only one plane of vibration is allowed to pass through.
  • After passing through the analyzer, the intensity is further subjected to the cosine-square law, detailed by Malus's Law.
  • The final intensity after the analyzer can be manipulated by changing the angle \( \theta \) between the polarizer and analyzer.
Understanding light intensity in these terms allows us to predict and control how bright or dim the light will be after undergoing polarization.
It is a practical aspect in designing lighting systems and performing precise optical measurements.

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

(a) In a double-slit experiment, if the distance from the double slits to the screen is increased, the separation between the adiacent maxima will (1) increase, (2) decrease, (3) remain the same. Explain. (b) Yellow-green light \((\lambda=550 \mathrm{nm})\) illuminates a double-slit separated by \(1.75 \times 10^{-4} \mathrm{~m} .\) If the screen is located \(2.00 \mathrm{~m}\) from the slits, determine the separation between the adjacent maxima. (c) What if the screen is located \(3.00 \mathrm{~m}\) from the slits?

The angle of incidence is adjusted so there is maximum linear polarization for the reflected light from a transparent piece of plastic in air. (a) There is (1) no, (2) maximum, or (3) some light transmitted through the plastic. Explain. (b) If the index of refraction of the plastic is 1.40 , what would be the angle of refraction in the plastic?

A teacher standing in a doorway \(1.0 \mathrm{~m}\) wide blows a whistle with a frequency of \(1000 \mathrm{~Hz}\) to summon children from the playground (v Fig. 24.31 ). Two boys are playing on the swings \(20 \mathrm{~m}\) away from the school building. One boy is at an angle of \(0^{\circ}\) and another one at \(19.6^{\circ}\) from a line normal to the doorway. Taking the speed of sound in air to be \(335 \mathrm{~m} / \mathrm{s}\), which boy may not hear the whisle? Prove your answer.

In a single-slit diffraction pattern using light of wavelength \(550 \mathrm{nm}\), the second-order minimum is measured to be at \(0.32^{\circ} .\) What is the slit width?

A thin air wedge between two flat glass plates forms bright and dark interference bands when illuminated with normally incident monochromatic light. (See Fig. 24.9.) (a) Show that the thickness of the air wedge changes by \(\lambda / 2\) from one bright band to the next, where \(\lambda\) is the wavelength of the light. (b) What would be the change in the thickness of the wedge between bright bands if the space were filled with a liquid with an index of refraction \(n ?\)
See all solutions

Recommended explanations on Physics Textbooks

Electricity and Magnetism

Read Explanation

Fluids

Read Explanation

Circular Motion and Gravitation

Read Explanation

Translational Dynamics

Read Explanation

Quantum Physics

Read Explanation

Magnetism

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.