Physics for Scientists and Engineers, Technology Update (No access codes included)
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN: 9781305116399
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 36, Problem 36.94CP

A zoom lens system is a combination of lenses that produces a variable magnification of a fixed object as it maintains a fixed image position. The magnification is varied by moving one or more lenses along the axis. Multiple lenses are used in practice, but the effect of zooming in on an object can be demonstrated with a simple two-lens system. An object, two converging lenses, and a screen are mounted on an optical bench. Lens 1, which is to the right of the object, has a focal length of f1 = 5.00 cm, and lens 2, which is to the right of the first lens, has a focal length of f2 = 10.0 cm. The screen is to the right of lens 2. Initially, an object is situated at a distance of 7.50 cm to the left of lens 1, and the image formed on the screen has a magnification of +1.00. (a) Find the distance between the object and the screen. (b) Both lenses are now moved along their common axis while the object and the screen maintain fixed positions until the image formed on the screen has a magnification of +3.00. Find the displacement of each lens from its initial position in part (a). (c) Can the lenses be displaced in more than one way?

(a)

Expert Solution
Check Mark
To determine
The distance between the object and the screen.

Answer to Problem 36.94CP

The distance between the object and the screen is 67.5cm .

Explanation of Solution

Given info: The focal length of the left and right lenses are f1=5.00cm and f2=10.0cm . The object distance is 7.50cm to the left of the lens 1. The magnification of the image is +1.00 .

Write the expression of thin lens equation for lens 1.

1q1=1f11p1

Here,

p1 is the object distance.

q1 is the image distance.

Substitute 5.00cm for f1 and 7.50cm for p1 in above equation.

1q1=15.00cm17.50cmq1=15cm

Write the expression for magnification.

M1=q1p1

Substitute 15cm for q1 and 7.50cm for p1 in above equation.

M1=15cm7.50cm=2

Write the expression of magnification for a combination of two lenses.

M=M1M2

Substitute 2 for M1 and 1 for M in above equation.

1=(2)M2M2=12

Write the expression to calculate the magnification for lens 2.

M2=q2p2

Substitute 12 for M2 in above equation.

12=q2p2p2=2q2 (1)

Write the expression of thin lens equation for lens 2.

1p2+1q2=1f2

Here,

p2 is the object distance from the lens 2.

q2 is the image distance from the lens 2.

Substitute 2q2 for p2 and 10.00cm for f2 in above equation.

12q2+1q2=110.00cmq2=15cm

Substitute 15cm for q2 in equation (1).

p2=2×15cm=30cm

The distance between the object and the screen is,

D=p1+q1+p2+q2

Substitute 7.5cm for p1 , 15cm for q1 , 30cm for p2 and 15cm for q2 in above equation.

D=7.5cm+15cm+30cm+15cm=67.5cm

Thus, the distance between the object and the screen is 67.5cm .

Conclusion:

Therefore, the distance between the object and the screen is 67.5cm .

(b)

Expert Solution
Check Mark
To determine
The displacement of each lens from its initial position.

Answer to Problem 36.94CP

The displacement of each lens from its initial position is 1.28cm and 17.7cm or 0.927cm and 4.44cm .

Explanation of Solution

Given info: The focal length of the left and right lenses are f1=5.00cm and f2=10.0cm . The object distance is 7.50cm to the left of the lens 1. The magnification of the image is +3.00 .

Write the expression of thin lens equation for lens 1.

1p1'+1q1'=1f1

Here,

p1' is the object distance from the lens 1.

q1' is the image distance from the lens1.

Substitute 5.00cm for f1 in above equation.

1p1'+1q1'=15.00cmq1'=5p1'p1'5

Write the expression of magnification for lens 1.

M1'=q1'p1'

Substitute 5p1'p1'5 for q1' in above equation.

M1'=5p1'p1'5p1'=5p1'5

Write the expression of magnification for the combination of lenses.

M'=M1'M2'M2'=M'M1'

Substitute 3 for M' and 5p1'5 for M1' in above equation.

M2'=35p1'5=35(p1'5)

Write the expression to calculate the magnification of lens 2.

M2'=q2'p2'

Substitute 35(p1'5) for M2' in above equation.

35(p1'5)=q2'p2'q2'=35p2'(p1'5) (2)

Write the expression of lens equation for lens 2.

1p2'+1q2'=1f2

Substitute 35p2'(p1'5) for q2' and 10cm for f2 in above equation.

1p2'+135p2'(p1'5)=110cmp2'=10(3p1'10)3(p1'5)

Substitute 10(3p1'10)3(p1'5) for p2' in equation (2).

q2'=35[10(3p1'10)3(p1'5)](p1'5)=2(3p1'10) (3)

The distance between the object and the screen is,

D=p1'+q1'+p2'+q2'

Substitute 5p1'p1'5 for q1' , 10(3p1'10)3(p1'5) for p2' , 2(3p1'10) for q2' and 67.5cm for D in above equation.

p1'+5p1'p1'5+10(3p1'10)3(p1'5)+2(3p1'10)=67.5cm[[3(p1'5)]p1'+15p1'+10(3p1'10)+2(3p1'10)[3(p1'5)]]=67.5[3(p1'5)][3(p1')2+30p1'100+18(p1')2150p1'+300202.5p1'+1012.5]=021(p1')2322.5p1'+1212.5=0

Solve the above quadratic equation to find the value of p1' .

21(p1')2322.5p1'+1212.5=0(p1'8.784)(p1'6.573)=0p1'=8.784cmp1'=6.573cm

When the value of p1' is, 8.784cm .

The displacement of object is,

p1'p1=8.784cm7.50cm=1.28cm

Substitute 8.784cm for p1' in equation (3).

q2'=2(3×8.784cm10)=32.7cm

The displacement of the image is,

q2'q2=32.7cm-15.0cm=17.7cm

When the value of p1' is, 6.573cm .

The displacement of object is,

p1'p1=6.573cm7.50cm=0.927cm

Substitute 6.573cm for p1' in equation (3).

q2'=2(3×6.573cm10)=19.44cm

The displacement of the image is,

q2'q2=19.44cm-15.0cm=4.44cm

Thus, the displacement of each lens from its initial position is 1.28cm and 17.7cm or 0.927cm and 4.44cm .

Conclusion:

Therefore, the displacement of each lens from its initial position is 1.28cm and 17.7cm or 0.927cm and 4.44cm .

(c)

Expert Solution
Check Mark
To determine
Whether the lens can be displaced by more than one way.

Answer to Problem 36.94CP

It is possible to displace the lens in more than one way.

Explanation of Solution

Given info: The focal length of the left and right lenses are f1=5.00cm and f2=10.0cm . The object distance is 7.50cm to the left of the lens 1. The magnification of the image is +1.00 .

Yes the lens can be displaced in more than one way.

The first lens can be displaced 1.28cm far from the object and the second lens can be moved by 17.7cm distance toward the object.

Another way is, the first lens can be moved 0.927cm toward the object and the second lens can be moved by 4.44cm distance toward the object.

Thus, it is possible to displace the lens in more than one way.

Conclusion:

Therefore, it is possible to displace the lens in more than one way.

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 36 Solutions

Physics for Scientists and Engineers, Technology Update (No access codes included)

Ch. 36 - An object is located 50.0 cm from a converging...Ch. 36 - Prob. 36.4OQCh. 36 - A converging lens in a vertical plane receives...Ch. 36 - Prob. 36.6OQCh. 36 - Prob. 36.7OQCh. 36 - Prob. 36.8OQCh. 36 - A person spearfishing from a boat sees a...Ch. 36 - Prob. 36.10OQCh. 36 - A converging lens made of crown glass has a focal...Ch. 36 - A converging lens of focal length 8 cm forms a...Ch. 36 - Prob. 36.13OQCh. 36 - An object, represented by a gray arrow, is placed...Ch. 36 - Prob. 36.1CQCh. 36 - Prob. 36.2CQCh. 36 - Why do some emergency vehicles have the symbol...Ch. 36 - Prob. 36.4CQCh. 36 - Prob. 36.5CQCh. 36 - Explain why a fish in a spherical goldfish bowl...Ch. 36 - Prob. 36.7CQCh. 36 - Lenses used in eyeglasses, whether converging or...Ch. 36 - Suppose you want to use a converging lens to...Ch. 36 - Consider a spherical concave mirror with the...Ch. 36 - In Figures CQ36.11a and CQ36.11b, which glasses...Ch. 36 - Prob. 36.12CQCh. 36 - Prob. 36.13CQCh. 36 - Prob. 36.14CQCh. 36 - Prob. 36.15CQCh. 36 - Prob. 36.16CQCh. 36 - Prob. 36.17CQCh. 36 - Determine the minimum height of a vertical flat...Ch. 36 - In a choir practice room, two parallel walls are...Ch. 36 - (a) Does your bathroom mirror show you older or...Ch. 36 - Prob. 36.4PCh. 36 - A periscope (Fig. P35.3) is useful for viewing...Ch. 36 - Two flat mirrors have their reflecting surfaces...Ch. 36 - Two plane mirrors stand facing each other, 3.00 m...Ch. 36 - An object is placed 50.0 cm from a concave...Ch. 36 - A concave spherical mirror has a radius of...Ch. 36 - An object is placed 20.0 cm from a concave...Ch. 36 - A convex spherical mirror has a radius of...Ch. 36 - Prob. 36.12PCh. 36 - An object of height 2.00 cm is placed 30.0 cm from...Ch. 36 - A dentist uses a spherical mirror to examine a...Ch. 36 - A large hall in a museum has a niche in one wall....Ch. 36 - Why is the following situation impossible? At a...Ch. 36 - Prob. 36.17PCh. 36 - A certain Christmas tree ornament is a silver...Ch. 36 - (a) A concave spherical mirror forms an inverted...Ch. 36 - (a) A concave spherical mirror forms ail inverted...Ch. 36 - An object 10.0 cm tall is placed at the zero mark...Ch. 36 - A concave spherical mirror has a radius of...Ch. 36 - A dedicated sports car enthusiast polishes the...Ch. 36 - A convex spherical mirror has a focal length of...Ch. 36 - A spherical mirror is to be used to form an image...Ch. 36 - Review. A ball is dropped at t = 0 from rest 3.00...Ch. 36 - You unconsciously estimate the distance to an...Ch. 36 - Prob. 36.28PCh. 36 - One end of a long glass rod (n = 1.50) is formed...Ch. 36 - A cubical block of ice 50.0 cm on a side is placed...Ch. 36 - Prob. 36.31PCh. 36 - Prob. 36.32PCh. 36 - A flint glass, plate rests on the bottom of an...Ch. 36 - Figure P35.20 (page 958) shows a curved surface...Ch. 36 - Prob. 36.35PCh. 36 - Prob. 36.36PCh. 36 - A goldfish is swimming at 2.00 cm/s toward the...Ch. 36 - A thin lens has a focal length of 25.0 cm. Locate...Ch. 36 - An object located 32.0 cm in front of a lens forms...Ch. 36 - An object is located 20.0 cm to the left of a...Ch. 36 - The projection lens in a certain slide projector...Ch. 36 - An objects distance from a converging lens is 5.00...Ch. 36 - A contact lens is made of plastic with an index of...Ch. 36 - A converging lens has a focal length of 10.0 cm....Ch. 36 - A converging lens has a focal length of 10.0 cm....Ch. 36 - A diverging lens has a focal length of magnitude...Ch. 36 - Prob. 36.47PCh. 36 - Suppose an object has thickness dp so that it...Ch. 36 - The left face of a biconvex lens has a radius of...Ch. 36 - In Figure P35.30, a thin converging lens of focal...Ch. 36 - An antelope is at a distance of 20.0 m from a...Ch. 36 - Prob. 36.52PCh. 36 - A 1.00-cm-high object is placed 4.00 cm to the...Ch. 36 - The magnitudes of the radii of curvature are 32.5...Ch. 36 - Two rays traveling parallel to the principal axis...Ch. 36 - Prob. 36.56PCh. 36 - Figure 35.34 diagrams a cross section of a camera....Ch. 36 - Josh cannot see objects clearly beyond 25.0 cm...Ch. 36 - Prob. 36.59PCh. 36 - A person sees clearly wearing eyeglasses that have...Ch. 36 - Prob. 36.61PCh. 36 - A certain childs near point is 10.0 cm; her far...Ch. 36 - A person is to be fitted with bifocals. She can...Ch. 36 - A simple model of the human eye ignores its lens...Ch. 36 - A patient has a near point of 45.0 cm and far...Ch. 36 - A lens that has a focal length of 5.00 cm is used...Ch. 36 - The distance between the eyepiece and the...Ch. 36 - The refracting telescope at the Yerkes Observatory...Ch. 36 - A certain telescope has an objective mirror with...Ch. 36 - Astronomers often take photographs with the...Ch. 36 - Prob. 36.71APCh. 36 - A real object is located at the zero end of a...Ch. 36 - The distance between an object and its upright...Ch. 36 - Prob. 36.74APCh. 36 - Andy decides to use an old pair of eyeglasses to...Ch. 36 - Prob. 36.76APCh. 36 - The lens and mirror in Figure P36.77 are separated...Ch. 36 - Two converging lenses having focal lengths of f1 =...Ch. 36 - Figure P36.79 shows a piece of glass with index of...Ch. 36 - Prob. 36.80APCh. 36 - The object in Figure P36.81 is midway between the...Ch. 36 - In many applications, it is necessary to expand or...Ch. 36 - Prob. 36.83APCh. 36 - Prob. 36.84APCh. 36 - Two lenses made of kinds of glass having different...Ch. 36 - Why is the following situation impossible?...Ch. 36 - An object is placed 12.0 cm to the left of a...Ch. 36 - An object is placed a distance p to the left of a...Ch. 36 - An observer to the right of the mirror-lens...Ch. 36 - In a darkened room, a burning candle is placed...Ch. 36 - Prob. 36.91APCh. 36 - An object 2.00 cm high is placed 40.0 cm to the...Ch. 36 - Assume the intensity of sunlight is 1.00 kW/m2 at...Ch. 36 - A zoom lens system is a combination of lenses that...Ch. 36 - Figure P36.95 shows a thin converging lens for...Ch. 36 - A floating strawberry illusion is achieved with...Ch. 36 - Consider the lensmirror arrangement shown in...
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
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
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
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
Convex and Concave Lenses; Author: Manocha Academy;https://www.youtube.com/watch?v=CJ6aB5ULqa0;License: Standard YouTube License, CC-BY