/*! 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 73 An object \(8.0 \mathrm{cm}\) hi... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 23: Problem 73

An object \(8.0 \mathrm{cm}\) high forms a virtual image \(3.5 \mathrm{cm}\) high located \(4.0 \mathrm{cm}\) behind a mirror. (a) Find the object distance. (b) Describe the mirror: is it plane, convex, or concave? (c) What are its focal length and radius of curvature?

Short Answer

Expert verified
What are the object distance, focal length, and radius of curvature? This is a convex mirror with an object distance of 9.143 cm, a focal length of 12.308 cm, and a radius of curvature of 24.615 cm.

Step by step solution

01

Calculate the Magnification Ratio

The magnification ratio (M) is the ratio of the image height (hi) to the object height (ho). We can calculate it by: $$ M = \frac{h_i}{h_o} $$ For this problem, \(h_o = 8.0\,\text{cm}\) and \(h_i = 3.5\,\text{cm}\). Plugging the values we get: $$ M = \frac{3.5}{8.0} $$
02

Determine the type of mirror

If the magnification ratio is positive, then the mirror is a virtual mirror and consequently, it is a convex mirror. If it is negative, then it is a concave mirror. In our calculation: $$ M = \frac{3.5}{8.0} > 0 $$ Since the magnification ratio is positive, the mirror is a convex mirror.
03

Calculate the object distance (do)

Since we know the magnification ratio (M), we can rewrite the magnification formula for a mirror as: $$ M = \frac{-d_i}{d_o} $$ We are given the image distance (\(d_i = -4.0\,\text{cm}\), negative because it is behind the mirror). So we can solve for the object distance (do): $$ d_o = -\frac{d_i}{M} $$ Plugging the values, we get: $$ d_o = -\frac{-4.0}{\frac{3.5}{8.0}} $$
04

Calculate the focal length (f) using the mirror equation

The mirror equation can be written as: $$ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} $$ We have calculated \(d_o\) and we are given \(d_i\). So we can solve for the focal length (f): $$ f = \frac{1}{\frac{1}{d_o} + \frac{1}{d_i}} $$ Plugging the values of \(d_o\) and \(d_i\), we can find the value of \(f\).
05

Calculate the radius of curvature (R)

The radius of curvature (R) is twice the focal length (f) for a mirror. So we can calculate it as: $$ R = 2f $$ Plugging in the value of focal length (f) that we calculated in step 4, we can find the radius of curvature. Now, you have the object distance (d_o), the type of mirror (convex), the focal length (f), and the radius of curvature (R).

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

A ray of light passes from air through dense flint glass and then back into air. The angle of incidence on the first glass surface is \(60.0^{\circ} .\) The thickness of the glass is \(5.00 \mathrm{mm} ;\) its front and back surfaces are parallel. How far is the ray displaced as a result of traveling through the glass?
A radar station is located at a height of \(24.0 \mathrm{m}\) above the shoreline. When the radar is aimed at a spot \(150.0 \mathrm{m}\) out to sea, it detects a whale at the bottom of the ocean. If it takes \(2.10 \mu \mathrm{s}\) for the radar to send out a beam and receive it again, how deep is the ocean where the whale is swimming?
A diamond in air is illuminated with white light. On one particular facet, the angle of incidence is \(26.00^{\circ} .\) Inside the diamond, red light \((\lambda=660.0 \mathrm{nm}\) in vacuum) is refracted at \(10.48^{\circ}\) with respect to the normal; blue light $(\lambda=470.0 \mathrm{nm} \text { in vacuum })\( is refracted at \)10.33^{\circ} .$ (a) What are the indices of refraction for red and blue light in diamond? (b) What is the ratio of the speed of red light to the speed of blue light in diamond? (c) How would a diamond look if there were no dispersion?
Sunlight strikes the surface of a lake at an angle of incidence of \(30.0^{\circ} .\) At what angle with respect to the normal would a fish see the Sun?
In a subway station, a convex mirror allows the attendant to view activity on the platform. A woman \(1.64 \mathrm{m}\) tall is standing \(4.5 \mathrm{m}\) from the mirror. The image formed of the woman is \(0.500 \mathrm{m}\) tall. (a) What is the radius of curvature of the mirror? (b) The mirror is \(0.500 \mathrm{m}\) in diameter. If the woman's shoes appear at the bottom of the mirror, does her head appear at the top-in other words, does the image of the woman fill the mirror from top to bottom? Explain.
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Measurements

Read Explanation

Dynamics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Magnetism

Read Explanation

Further Mechanics and Thermal 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.