/*! 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 3 A plate glass window \((n=1.5)\)... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 3

A plate glass window \((n=1.5)\) has a thickness of \(4.0 \times 10^{-3} \mathrm{~m}\). How long does it take light to pass perpendicularly through the plate?

Short Answer

Expert verified
The time is \(2.0 \times 10^{-11}\) seconds.

Step by step solution

01

Identify Given Values

We know that the refractive index of the glass, denoted as \(n\), is 1.5. The thickness of the glass \(d\) is \(4.0 \times 10^{-3}\) meters. We need to find the time \(t\) it takes for light to pass through the glass.
02

Determine the Speed of Light in Glass

The speed of light in a medium \(v\) can be calculated using the equation:\[v = \frac{c}{n}\]where \(c\) is the speed of light in a vacuum \((3.0 \times 10^8 \text{ m/s})\). Substitute the given value of \(n\):\[v = \frac{3.0 \times 10^8 \text{ m/s}}{1.5} = 2.0 \times 10^8 \text{ m/s}\]
03

Calculate Time Taken Using Speed and Distance

To find the time \(t\) it takes for light to travel through the glass, use the formula:\[t = \frac{d}{v}\]Substitute the values of \(d\) and \(v\):\[t = \frac{4.0 \times 10^{-3} \text{ m}}{2.0 \times 10^8 \text{ m/s}} = 2.0 \times 10^{-11} \text{ s}\]
04

Conclusion

The time taken for light to pass perpendicularly through the glass plate is \(2.0 \times 10^{-11}\) seconds.

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.

Speed of Light
The speed of light, denoted by the symbol \(c\), is a fundamental constant of nature. In a vacuum, light travels at a speed of approximately \(3.0 \times 10^8\) meters per second. This speed is incredibly fast. It allows light to cover vast distances in short periods of time.

The importance of the speed of light extends beyond just understanding how light travels. It is a crucial component in many scientific equations and theories, such as Einstein's theory of relativity. In our everyday world, knowing the speed of light helps us calculate how long it takes light to travel through different materials, which is invaluable in optics.
  • In a vacuum, light travels at \(3.0 \times 10^8\) m/s.
  • The speed changes when light enters different materials.
  • The calculation of light's speed in mediums is critical in technology and science.
Refractive Index
The refractive index, often represented by \(n\), is a measure of how much a substance slows down light. When light transitions from one medium to another, such as from air to glass, it changes speed due to the refractive index of the new medium.

The refractive index is calculated using the formula \(n = \frac{c}{v}\), where \(c\) is the speed of light in a vacuum, and \(v\) is the speed of light in the medium. A higher refractive index indicates the medium slows light more. For example, glass with \(n = 1.5\) reduces the speed of light compared to air, which has a refractive index close to 1.
  • Glass with \(n = 1.5\) slows light to \(2.0 \times 10^8\) m/s.
  • Refractive index is a dimensionless number.
  • It helps determine how much light bends when entering a different medium.
Medium
A medium is any material through which light can travel. Common mediums include air, water, and glass. Each medium has unique properties that affect the speed and direction of light passing through it.

The optical properties of a medium are largely dependent on its refractive index. When light enters a medium with a different refractive index, its speed and direction change, which can be observed as refraction. This change is essential in designing lenses and other optical devices.
  • Light travels slower in a denser medium.
  • Understanding mediums is crucial for optics and various technologies.
  • Changes in speed and direction of light in a medium are due to refraction.

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 nearsighted person wears contacts to correct for a far point that is only \(3.62 \mathrm{~m}\) from his eyes. The near point of his unaided eyes is \(25.0 \mathrm{~cm}\) from his eyes. If he does not remove the lenses when reading, how close can he hold a book and see it clearly?

Bill is farsighted and has a near point located \(125 \mathrm{~cm}\) from his eyes. Anne is also farsighted, but her near point is \(75.0 \mathrm{~cm}\) from her eyes. Both have glasses that correct their vision to a normal near point \((25.0 \mathrm{~cm}\) from the eyes), and both wear the glasses 2.0 \(\mathrm{cm}\) from the eyes. Relative to the eyes, what is the closest object that can be seen clearly (a) by Anne when she wears Bill's glasses and (b) by Bill when he wears Anne's glasses?

A refracting telescope has an angular magnification of \(-83.00 .\) The length of the barrel is \(1.500 \mathrm{~m}\). What are the focal lengths of (a) the objective and (b) the eyepiece?

A beam of light is traveling in air and strikes a material. The angles of incidence and refraction are \(63.0^{\circ}\) and \(47.0^{\circ}\), respectively. Obtain the speed of light in the material.

The drawing shows a ray of light traveling through three materials whose surfaces are parallel to each other. The refracted rays (but not the reflected rays) are shown as the light passes through each material. Taking into account the relative sizes of the angles of incidence and refraction, rank the materials according to their indices of refraction, greatest first. Provide reasons for your ranking. A ray of light strikes the \(a-b\) interface at a \(50.0^{\circ}\) angle of incidence. The index of refraction of material \(a\) is \(n_{a}=1.20\). The angles of refraction in materials \(b\) and \(c\) are, respectively, \(45.0^{\circ}\) and \(56.7^{\circ}\). Find the indices of refraction in these two media. Verify that your answers are consistent with your answers to the Concept Qucstion.
See all solutions

Recommended explanations on Physics Textbooks

Magnetism

Read Explanation

Physics of Motion

Read Explanation

Translational Dynamics

Read Explanation

Energy Physics

Read Explanation

Kinematics Physics

Read Explanation

Oscillations

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.