Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

What is the focal length of a makeup mirror that produces a magnification of \(1.50\)when a person’s face is \(12.0\;cm\) away? Explicitly show how you follow the steps in the Problem-Solving Strategy for Mirrors.

Short Answer

Expert verified

The value of the focal length of the given makeup mirror is \(0.36\;m\).

Step by step solution

01

Definition of focal length

The focal length of an optical system is the inverse of the system's optical power; it measures how strongly the system converges or diverges light. A system with a positive focal length converges light, while a system with a negative focal length diverges light.

02

Information Provided

  • The magnification value:\(1.50\).
  • Distance between lens and person’s face: \(12.0\;cm\).
03

Calculation for the focal length of the mirror

Use the magnification equation:

\(m = - \dfrac{{{d_i}}}{{{d_o}}}\)

where \(m\) denotes the magnification, \({d_o}\) denotes the distance between the object and the lens, and\({d_i}\) denotes the distance from the lens to the projected image that is in focus.

To find the image distance\({d_i}\)and then use it to solve the equation of the focal length via\(\dfrac{1}{f} = \dfrac{1}{{{d_i}}} + \dfrac{1}{{{d_o}}}\).

Where \(f\) denotes the lens's focal length, \({d_o}\) denotes the distance between the object and the lens, and \({d_i}\) denotes the distance from the lens to the projected image that is in focus.

\(\begin{aligned}f &= {\left( {\dfrac{{ - 1}}{{m{d_o}}} + \dfrac{1}{{{d_o}}}} \right)^{ - 1}}\\f &= {\left( {\dfrac{{ - 1}}{{1.50 \times 0.12\;m}} + \dfrac{1}{{0.12\;m}}} \right)^{ - 1}}\\f &= 0.36\;m\end{aligned}\)

Therefore, the value of the focal length is \(0.36\;m\).

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 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

How far from a piece of paper must you hold your father’s 2.25 Dreading glasses to try to burn a hole in the paper with sunlight?

Consider a \(250{\rm{ }}W\) heat lamp fixed to the ceiling in a bathroom. If the filament in one light burns out then the remaining three still work. Construct a problem in which you determine the resistance of each filament in order to obtain a certain intensity projected on the bathroom floor. The ceiling is \(3.0{\rm{ }}m\) high. The problem will need to involve concave mirrors behind the filaments. Your instructor may wish to guide you on the level of complexity to consider in the electrical components.

The Ray Aspect of Light

Suppose a man stands in front of a mirror as shown in Figure 25.50. His eyes are 1.65 mabove the floor, and the top of his head is 0.13 mhigher. Find the height above the floor of the top and bottom of the smallest mirror in which he can see both the top of his head and his feet. How is this distance related to the man's height?

Image Caption

Figure 25.50A full-length mirror is one in which you can see all of yourself. It need not be as big as you, and its size is independent of your distance from it.

A light ray entering an optical fibre surrounded by air is first refracted and then reflected as shown in Figure 25.56. Show that if the fibre is made from crown glass, any incident ray will be totally internally reflected.

Figure 25.56A light ray enters the end of a fibre, the surface of which is perpendicular to its sides. Examine the conditions under which it may be totally internally reflected.

Under what circumstances will an image be located at the focal point of a lens or mirror?

See all solutions

Recommended explanations on Physics Textbooks

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