Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 38, Problem 31SP

Determine the nature, position, and transverse magnification of the image formed by a thin converging lens of focal length +100 cm when the object distance from the lens is (a) 150 cm, (b) 75.0 cm.

(a)

Expert Solution
Check Mark
To determine

The nature, position, and transverse magnification of an image formed by a thin converging lens of focal length 100 cm if the object distance is 150 cm.

Answer to Problem 31SP

Solution:

Inverted, real image, 300 cm beyond the lens, and magnified by 2:1.

Explanation of Solution

Given data:

The object distance is 150 cm.

The focal length of the lens is 100 cm.

Formula used:

Write the thin lens equation.

1f=1so+1si

Rearrange the above equation.

1si=1f1so

Here, f is the focal length of the lens, so is the distance of the object from the lens, and si is the distance of the image from the lens.

Write the expression for the magnification of an image.

MT=siso

Here, MT is the magnification of the image, si is the distance of the image from the lens, and so is the distance of the object from the lens.

Explanation:

Recall the thin lens equation.

1si=1f1so

Substitute 100 cm for f and 150 cm for so

1si=1100 cm1150 cm

Solve for si.

si=300 cm

Write the expression for the magnification of an image.

MT=siso

Substitute 300 cm for si and 150 cm for so

MT=300 cm150 cm=2

Here, negative sign shows that the image is inverted. Therefore, the ration of the object’s magnification will be 2:1.

Conclusion:

Therefore, the image shall be formed at a distance of 300 cm from the lens( on the left side) and shall be inverted, real, and magnified. The magnification of the image is 2:1.

(b)

Expert Solution
Check Mark
To determine

The nature, position and transverse magnification of an image formed by a thin converging lens of focal length 100 cm if the object distance is 75.0 cm.

Answer to Problem 31SP

Solution:

300 cm on the right side of the lens and erect, virtual, magnified by 4:1.

Explanation of Solution

Given data:

The object distance is 75.0 cm.

The focal length of the lens is 100 cm.

Formula used:

Write the thin lens equation.

1f=1so+1si

Rearrange the above equation.

1si=1f1so

Here, f is the focal length of the lens, so is the distance of the object from the lens, and si is the distance of the image from the lens.

Write the expression for the magnification of an image.

MT=siso

Here, MT is the magnification of the image, si is the distance the image from the lens, and so is the distance of the object from the lens.

Explanation:

Recall the thin lens equation.

1si=1f1so

Substitute 100 cm for f and 75.0 cm for so

1si=1100 cm175.0 cm

Solve for si.

si=300 cm

Write the expression for the magnification of an image.

MT=siso

Substitute 300 cm for si and 75.0 cm for so

MT=(300 cm)75.0 cm       = +4

Here, positive sign shows that the image is erect. Therefore, the ration of the object’s magnification will be 4:1.

Conclusion:

The image shall be formed at a distance of 300 cm from the lens( on the right side) and shall be erect, virtual, and highly magnified. The magnification of the image is 4:1.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 38 Solutions

Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)

Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Convex and Concave Lenses; Author: Manocha Academy;https://www.youtube.com/watch?v=CJ6aB5ULqa0;License: Standard YouTube License, CC-BY