Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 33: Problem 76

A classmate claims that by using a \(40.0-\mathrm{cm}\) focal length mirror, he can project onto a screen a \(10.0-\mathrm{cm}\) tall bird locat ed 100 . \(\mathrm{m}\) away. He claims that the image will be no less than \(1.00 \mathrm{~cm}\) tall and inverted. Will he make good on his claim?

Short Answer

Expert verified
Answer: No, the student's claim is partially correct. Though the projected image is indeed inverted, it is smaller than 1 cm tall (approximately 0.421 cm).

Step by step solution

01

Identify the given information

We are given: 1. Focal length of the mirror (f) = 40 cm 2. Object distance from the mirror (d_o) = 100 m (convert it to cm) 3. Object height (h_o) = 10 cm We need to find the height of the image (h_i) and verify if it is inverted.
02

Convert the distance to a matching unit

Convert the object distance from meters to centimeters: d_o = 100 m * 100 cm/m = 10,000 cm
03

Use the mirror equation to find the image distance (d_i)

The mirror equation is: 1/f = 1/d_o + 1/d_i Rearrange to solve for d_i: 1/d_i = 1/f - 1/d_o Substitute the values: 1/d_i = 1/(40 cm) - 1/(10,000 cm) Now, calculate the value of d_i: d_i = 1/((1/40 - 1/10000)) ≈ 42.11 cm
04

Use the magnification equation to find the image height (h_i)

The magnification equation is: M = h_i / h_o = -d_i / d_o We want to find h_i, so rearrange the equation: h_i = h_o * (-d_i / d_o) Substitute the values: h_i = (10 cm) * (-42.11 cm / 10,000 cm) Calculate the value of h_i: h_i ≈ -0.421 cm
05

Determine if the claim is correct

From our calculations, we find that the height of the image (h_i) is approximately -0.421 cm, which means the image is indeed inverted (negative sign). However, the image is smaller than the claimed 1 cm (0.421 cm < 1 cm). Therefore, the claim is partially correct - the image is inverted, but it is smaller than 1 cm.

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.

Start your free trial

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

The objective lens in a laboratory microscope has a focal length of \(3.00 \mathrm{~cm}\) and provides an overall magnification of \(1.0 \cdot 10^{2} .\) What is the focal length of the eyepiece if the distance between the two lenses is \(30.0 \mathrm{~cm}\) ?

Some reflecting telescope mirrors utilize a rotating tub of mercury to produce a large parabolic surface. If the tub is rotating on its axis with an angular frequency \(\omega,\) show that the focal length of the resulting mirror is: \(f=g / 2 \omega^{2}\).

An object of height \(h\) is placed at a distance \(d_{0}\) on the left side of a converging lens of focal length \(f\left(f

The focal length of the lens of a camera is \(38.0 \mathrm{~mm}\). How far must the lens be moved to change focus from a person \(30.0 \mathrm{~m}\) away to one that is \(5.00 \mathrm{~m}\) away?

You visit your eye doctor and discover that you require lenses having a diopter value of -8.4 . Are you nearsighted or farsighted? With uncorrected vision, how far away from your eyes must you hold a book to read clearly?
See all solutions

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Read Explanation

Fluids

Read Explanation

Oscillations

Read Explanation

Engineering Physics

Read Explanation

Electric Charge Field and Potential

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.

Sign-up for free