Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 22: Problem 70

Polarized light of intensity \(I_{0}\) is incident on a pair of polarizing sheets. Let \(\theta_{1}\) and \(\theta_{2}\) be the angles between the direction of polarization of the incident light and the transmission axes of the first and second sheets, respectively. Show that the intensity of the transmitted light is $I=I_{0} \cos ^{2} \theta_{1} \cos ^{2}\left(\theta_{1}-\theta_{2}\right)$.

Short Answer

Expert verified
Answer: The intensity of the transmitted light can be found using the formula I = I₀ * cos²(θ₁) * cos²(θ₁ - θ₂).

Step by step solution

01

Intensity after the first sheet

To find the intensity after the first polarizing sheet, apply Malus' Law using the angle between the direction of polarization of the incident light (θ₁) and the transmission axis of the first sheet. Since the initial intensity is I₀, the intensity after the first sheet (I₁) is: I₁ = I₀ * cos²(θ₁)
02

Intensity after the second sheet

The intensity after the second sheet depends on both the first and the second sheet's transmission axes. Consider the angle between the first sheet's transmission axis (aligned with the transmitted light after the first sheet) and the second sheet's transmission axis, which is (θ₁ - θ₂). Now we apply Malus' Law again using this angle and the intensity after the first sheet (I₁): I = I₁ * cos²(θ₁ - θ₂)
03

Combining the results from both sheets

Now, substitute the expression for I₁ obtained in step 1 into the equation we derived in step 2: I = (I₀ * cos²(θ₁)) * cos²(θ₁ - θ₂) So, the intensity of the transmitted light is given as: I = I₀ * cos²(θ₁) * cos²(θ₁ - θ₂)

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

What must be the relative speed between source and receiver if the wavelength of an EM wave as measured by the receiver is twice the wavelength as measured by the source? Are source and observer moving closer together or farther apart?
Unpolarized light is incident on a system of three polarizers. The second polarizer is oriented at an angle of \(30.0^{\circ}\) with respect to the first and the third is oriented at an angle of \(45.0^{\circ}\) with respect to the first. If the light that emerges from the system has an intensity of $23.0 \mathrm{W} / \mathrm{m}^{2},$ what is the intensity of the incident light?
The magnetic field in a microwave traveling through vacuum has amplitude $4.00 \times 10^{-11} \mathrm{T}\( and frequency \)120 \mathrm{GHz}$. Find the amplitude and frequency of the electric field.
What is the frequency of the microwaves in a microwave oven? The wavelength is \(12 \mathrm{cm}\)
A police car's radar gun emits microwaves with a frequency of $f_{1}=36.0 \mathrm{GHz}$. The beam reflects from a speeding car, which is moving away at \(43.0 \mathrm{m} / \mathrm{s}\) with respect to the police car. The frequency of the reflected microwave as observed by the police is \(f_{2} .\) (a) Which is larger, \(f_{1}\) or \(f_{2} ?\) (b) Find the frequency difference \(f_{2}-f_{1}\) [Hint: There are two Doppler shifts. First think of the police as source and the speeder as observer. The speeding car "retransmits" a reflected wave at the same frequency at which it observes the incident wave. \(]\)
See all solutions

Recommended explanations on Physics Textbooks

Translational Dynamics

Read Explanation

Dynamics

Read Explanation

Force

Read Explanation

Medical Physics

Read Explanation

Famous Physicists

Read Explanation

Thermodynamics

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.

Sign-up for free