Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 1: Problem 75

A scuba diver sees light reflected from the water's surface. At what angle relative to the water's surface will this light be completely polarized?

Short Answer

Expert verified
The light reflected from the water's surface will be completely polarized at an angle of approximately \(36.9^\circ\) relative to the water's surface.

Step by step solution

01

Understand Brewster's Law

Brewster's Law states that when the angle between the reflected and refracted light rays is 90 degrees, the reflected light is completely polarized. The relationship between the angle of incidence (θ₁) and the angle of refraction (θ₂) is given by Brewster's Law: tan(θ₁) = n₂ / n₁ where n₁ is the refractive index of the first medium (air in this case) and n₂ is the refractive index of the second medium (water). For air, the refractive index is approximately 1, and for water, it is approximately 1.33.
02

Apply Snell's Law

Snell's Law relates the angle of incidence (θ₁), the angle of refraction (θ₂), and the refractive indexes of the two media (n₁ and n₂) as follows: n₁ * sin(θ₁) = n₂ * sin(θ₂) Since we know the refractive indexes, we can use Snell's Law to express the angle of refraction (θ₂) in terms of the angle of incidence (θ₁).
03

Substitute Brewster's Law into Snell's Law

Replace tan(θ₁) from Brewster's Law in the Snell's Law equation: 1 * sin(θ₁) = 1.33 * sin(arctan(1.33 / 1)) sin(θ₁) = 1.33 * sin(arctan(1.33))
04

Calculate the angle of incidence θ₁

Solve for the angle of incidence (θ₁): θ₁ = arcsin(1.33 * sin(arctan(1.33))) ≈ 53.1°
05

Determine the angle relative to the water's surface

The angle of incidence is measured from the normal (perpendicular) to the surface. To find the angle relative to the water's surface, subtract the angle of incidence from 90 degrees: Angle relative to the water's surface = 90° - 53.1° ≈ 36.9° The light reflected from the water's surface will be completely polarized at an angle of approximately 36.9 degrees relative to the water's surface.

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 is the speed of light in air? In crown glass?

Why is the index of refraction always greater than or equal to \(1 ?\)

By how much do the critical angles for red (660 nm) and violet (410 nm) light differ in a diamond surrounded by air?

When light is reflected at Brewster's angle from a smooth surface, it is \(100 \%\) polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be \(100 \%\) ?

At the end of Example \(1.7,\) it was stated that the intensity of polarized light is reduced to \(90.0 \%\) of its original value by passing through a polarizing filter with its axis at an angle of \(18.4^{\circ}\) to the direction of polarization. Verify this statement.
See all solutions

Recommended explanations on Physics Textbooks

Thermodynamics

Read Explanation

Rotational Dynamics

Read Explanation

Force

Read Explanation

Work Energy and Power

Read Explanation

Quantum Physics

Read Explanation

Space 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.

Sign-up for free