/*! 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 110 A person working on the transmis... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 26: Problem 110

A person working on the transmission of a car accidentally drops a bolt into a tray of oil. The oil is 5.00 cm deep. The bolt appears to be 3.40 cm beneath the surface of the oil, when viewed from directly above. What is the index of refraction of the oil?

Short Answer

Expert verified
The index of refraction of the oil is approximately 1.47.

Step by step solution

01

Understand the Apparent Depth

When light is refracted at the interface of two different media (in this case, oil and air), the actual depth of an object can appear smaller than it really is. This phenomenon can be described using the concept of the apparent depth.
02

Recall the Formula for Apparent Depth

The relationship between the actual depth, the apparent depth, and the index of refraction of the medium is given by the formula:\[ n = \frac{d_a}{d_o} \]where \( n \) is the index of refraction, \( d_a \) is the actual depth, and \( d_o \) is the apparent depth.
03

Plug in the Values

The actual depth \( d_a \) is 5.00 cm, and the apparent depth \( d_o \) is 3.40 cm. Substitute these values into the formula:\[ n = \frac{5.00}{3.40}\]
04

Calculate the Index of Refraction

Perform the division to find the index of refraction:\[ n = \frac{5.00}{3.40} \approx 1.47\]Thus, the index of refraction of the oil is approximately 1.47.

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.

Understanding Apparent Depth
When you look at an object submerged in a liquid, like when you see a bolt in a tray of oil, the depth at which the object appears to be is often different from its actual depth. This is known as the apparent depth. Light behaves in a curious way when it travels through different media, such as from oil to air. It bends due to a phenomenon called refraction.
  • Light speed changes as it moves from one medium to another.
  • This change in speed causes the light to bend, making objects look closer or further away than they actually are.
The apparent depth is important in fields such as optics and vision systems. By understanding this concept, engineers and scientists can create lenses and devices that take into account how light behaves, ensuring accurate observations and measurements.
The Process of Refraction
Refraction occurs when light travels between different mediums. This is common in everyday objects, like looking into a pool or a glass of water. Here's how it works in simple terms:
  • When light enters a denser medium (like oil from air), it slows down and bends towards the normal line, an imaginary line perpendicular to the surface.
  • This bending might cause the submerged objects to seem displaced from their actual position.
  • The extent of bending depends on the index of refraction, a unique property of each medium.
The degree of bending is crucial for understanding phenomena in optics, like the "broken" appearance of a pencil in a glass of water. Refraction is not only responsible for such visual tricks but also is foundational to technologies using lenses.
Applications in Optical Physics
Optical physics is a field dedicated to studying how light interacts with matter. Refraction is one of its many fascinating phenomena. Here's why it's important:
  • Instruments like microscopes and cameras rely on precise control and understanding of how light refracts through various materials to function effectively.
  • Optical fibers used in telecommunications utilize light refraction to transmit data efficiently over long distances.
  • Even our own eyes use refraction to focus light and form images on our retinas.
By mastering the principles of refraction, optical physicists can innovate and enhance the capabilities of various technologies. From creating corrective lenses to improving imaging systems, the applications of these principles are vast and impactful.

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

Bill is farsighted and has a near point located 125 cm from his eyes. Anne is also farsighted, but her near point is 75.0 cm from her eyes. Both have glasses that correct their vision to a normal near point (25.0 cm from the eyes), and both wear the glasses 2.0 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鈥檚 glasses and (b) by Bill when he wears Anne鈥檚 glasses?

A ray of sunlight is passing from diamond into crown glass; the angle of incidence is \(35.00^{\circ} .\) The indices of refraction for the blue and red components of the ray are: blue \(\left(n_{\text { diamood }}=2.444, n_{\text { cromgless }}=1.531\right)\) and red \(\left(n_{\text { dianood }}=2.410, n_{\text { crown glass }}=1.520\right) .\) Determine the angle between the refracted blue and red rays in the crown glass.

The back wall of a home aquarium is a mirror that is a distance of 40.0 cm away from the front wall. The walls of the tank are negligibly thin. A fish, swimming midway between the front and back walls, is being viewed by a person looking through the front wall. The index of refraction of air is nair 1.000 and that of water is n water 1.333. (a) Calculate the apparent distance between the fish and the front wall. (b) Calculate the apparent distance between the image of the fish and the front wall. The index of refraction of air is \(n_{\mathrm{air}}=1.000\) and that of water is \(n_{\text { water }}=1.333 .\) (a) Calculate the apparent distance between the fish and the front wall. (b) Calculate the apparent distance between the image of the fish and the front wall.

A camera is supplied with two interchangeable lenses, whose focal lengths are 35.0 and 150.0 mm. A woman whose height is 1.60 m stands 9.00 m in front of the camera. What is the height (including sign) of her image on the image sensor, as produced by (a) the 35.0-mm lens and (b) the 150.0-mm lens?

A converging lens \((f=25.0 \mathrm{cm})\) is used to project an image of an object onto a screen. The object and the screen are 125 \(\mathrm{cm}\) apart, and between them the lens can be placed at either of two locations. Find the two object distances.
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Measurements

Read Explanation

Geometrical and Physical Optics

Read Explanation

Translational Dynamics

Read Explanation

Electrostatics

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.