/*! 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 25 Total internal reflection occurs... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 30: Problem 25

Total internal reflection occurs at an interface between plastic and air at incidence angles greater than \(37^{\circ} .\) Find the plastic's refractive index.

Short Answer

Expert verified
The refractive index of the plastic is approximately 1.64.

Step by step solution

01

Understand the concept of total internal reflection

Total internal reflection occurs when a wave (such as a light wave) hits a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface. In the critical angle, the refracted wave is parallel to the boundary of the medium, passing from a more dense to a less dense medium. When the wave hits at an angle larger than the critical, the wave is completely reflected and none is refracted.
02

Apply Snell's Law to find the refractive index

Having in mind the critical angle for total internal reflection, apply Snell's law in such a way that the light is incident at the critical angle. They formula would be:\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \]Since total reflection is taking place, \(\theta_2\) equals \(90^{\circ}\) and thus \(\sin \theta_2 = 1\). This simplifies the equation to: \[ n_{1}= n_{2} / \sin \theta_{1} \]
03

Substitute the known values

Now you can use the given values: \(n_2 = 1\) (the refractive index for air) and \(\theta_1 = 37 ^{\circ}\). This would result in: \[ n_{1}= 1 / \sin 37^{\circ} \]

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!

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

An attempt to rework Example 30.4 with an isosceles prism results in imaginary numbers for the two angles of refraction. What could this mean?

Why do a diamond and an identically shaped piece of glass sparkle differently?

A cylindrical tank \(2.4 \mathrm{m}\) decp is full to the brim with water. Sunlight first hits part of the tank bottom when the rising Sun makes a \(22^{\circ}\) angle with the horizon. Find the tank's diameter.

For the interface between air (refractive index 1 ) and a material with refractive index \(n,\) show that the critical angle and the polarizing angle are related by \(\sin \theta_{\mathrm{c}}=\cot \theta_{\mathrm{p}}.\)

To what angular accuracy must two ostensibly perpendicular mirrors be aligned so that an incident ray returns within \(1^{\circ}\) of its incident direction?
See all solutions

Recommended explanations on Physics Textbooks

Torque and Rotational Motion

Read Explanation

Scientific Method Physics

Read Explanation

Nuclear Physics

Read Explanation

Solid State Physics

Read Explanation

Circular Motion and Gravitation

Read Explanation

Classical Mechanics

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.