<< Chapter < Page Chapter >> Page >

Summary

  • Two types of lenses are possible: converging and diverging. A lens that causes light rays to bend toward (away from) its optical axis is a converging (diverging) lens.
  • For a converging lens, the focal point is where the converging light rays cross; for a diverging lens, the focal point is the point from which the diverging light rays appear to originate.
  • The distance from the center of a thin lens to its focal point is called the focal length f .
  • Ray tracing is a geometric technique to determine the paths taken by light rays through thin lenses.
  • A real image can be projected onto a screen.
  • A virtual image cannot be projected onto a screen.
  • A converging lens forms either real or virtual images, depending on the object location; a diverging lens forms only virtual images.

Conceptual questions

You can argue that a flat piece of glass, such as in a window, is like a lens with an infinite focal length. If so, where does it form an image? That is, how are d i and d o related?

Got questions? Get instant answers now!

When you focus a camera, you adjust the distance of the lens from the film. If the camera lens acts like a thin lens, why can it not be a fixed distance from the film for both near and distant objects?

The focal length of the lens is fixed, so the image distance changes as a function of object distance.

Got questions? Get instant answers now!

A thin lens has two focal points, one on either side of the lens at equal distances from its center, and should behave the same for light entering from either side. Look backward and forward through a pair of eyeglasses and comment on whether they are thin lenses.

Got questions? Get instant answers now!

Will the focal length of a lens change when it is submerged in water? Explain.

Yes, the focal length will change. The lens maker’s equation shows that the focal length depends on the index of refraction of the medium surrounding the lens. Because the index of refraction of water differs from that of air, the focal length of the lens will change when submerged in water.

Got questions? Get instant answers now!

Problems

How far from the lens must the film in a camera be, if the lens has a 35.0-mm focal length and is being used to photograph a flower 75.0 cm away? Explicitly show how you follow the steps in the [link] .

Got questions? Get instant answers now!

A certain slide projector has a 100 mm-focal length lens. (a) How far away is the screen if a slide is placed 103 mm from the lens and produces a sharp image? (b) If the slide is 24.0 by 36.0 mm, what are the dimensions of the image? Explicitly show how you follow the steps in the [link] .

a. 1 d i + 1 d o = 1 f d i = 3.43 m ;
b. m = −33.33 , so that ( 2.40 × 10 −2 m ) ( 33.33 ) = 80.0 cm, and ( 3.60 × 10 −2 m ) ( 33.33 ) = 1.20 m 0.800 m × 1.20 m or 80.0 cm × 120 cm

Got questions? Get instant answers now!

A doctor examines a mole with a 15.0-cm focal length magnifying glass held 13.5 cm from the mole. (a) Where is the image? (b) What is its magnification? (c) How big is the image of a 5.00 mm diameter mole?

Got questions? Get instant answers now!

A camera with a 50.0-mm focal length lens is being used to photograph a person standing 3.00 m away. (a) How far from the lens must the film be? (b) If the film is 36.0 mm high, what fraction of a 1.75-m-tall person will fit on it? (c) Discuss how reasonable this seems, based on your experience in taking or posing for photographs.

a. 1 d o + 1 d i = 1 f d i = 5.08 cm ;
b. m = −1.695 × 10 −2 , so the maximum height is 0.036 m 1.695 × 10 −2 = 2.12 m 100% ;
c. This seems quite reasonable, since at 3.00 m it is possible to get a full length picture of a person.

Got questions? Get instant answers now!

A camera lens used for taking close-up photographs has a focal length of 22.0 mm. The farthest it can be placed from the film is 33.0 mm. (a) What is the closest object that can be photographed? (b) What is the magnification of this closest object?

Got questions? Get instant answers now!

Suppose your 50.0 mm-focal length camera lens is 51.0 mm away from the film in the camera. (a) How far away is an object that is in focus? (b) What is the height of the object if its image is 2.00 cm high?

a. 1 d o + 1 d i = 1 f d o = 2.55 m ;
b. h i h o = d i d o h o = 1.00 m

Got questions? Get instant answers now!

What is the focal length of a magnifying glass that produces a magnification of 3.00 when held 5.00 cm from an object, such as a rare coin?

Got questions? Get instant answers now!

The magnification of a book held 7.50 cm from a 10.0 cm-focal length lens is 3.00. (a) Find the magnification for the book when it is held 8.50 cm from the magnifier. (b) Repeat for the book held 9.50 cm from the magnifier. (c) Comment on how magnification changes as the object distance increases as in these two calculations.

a. Using 1 d o + 1 d i = 1 f , d i = −56.67 cm . Then we can determine the magnification, m = 6.67 . b. d i = −190 cm and m = + 20.0 ; c. The magnification m increases rapidly as you increase the object distance toward the focal length.

Got questions? Get instant answers now!

Suppose a 200 mm-focal length telephoto lens is being used to photograph mountains 10.0 km away. (a) Where is the image? (b) What is the height of the image of a 1000 m high cliff on one of the mountains?

Got questions? Get instant answers now!

A camera with a 100 mm-focal length lens is used to photograph the sun. What is the height of the image of the sun on the film, given the sun is 1.40 × 10 6 km in diameter and is 1.50 × 10 8 km away?

1 d o + 1 d i = 1 f d i = 1 ( 1 / f ) ( 1 / d o ) d i d o = 6.667 × 10 −13 = h i h o h i = −0.933 mm

Got questions? Get instant answers now!

Use the thin-lens equation to show that the magnification for a thin lens is determined by its focal length and the object distance and is given by m = f / ( f d o ) .

Got questions? Get instant answers now!

An object of height 3.0 cm is placed 5.0 cm in front of a converging lens of focal length 20 cm and observed from the other side. Where and how large is the image?

d i = −6.7 cm
h i = 4.0 cm

Got questions? Get instant answers now!

An object of height 3.0 cm is placed at 5.0 cm in front of a diverging lens of focal length 20 cm and observed from the other side. Where and how large is the image?

Got questions? Get instant answers now!

An object of height 3.0 cm is placed at 25 cm in front of a diverging lens of focal length 20 cm. Behind the diverging lens, there is a converging lens of focal length 20 cm. The distance between the lenses is 5.0 cm. Find the location and size of the final image.

83 cm to the right of the converging lens, m = −2.3 , h i = 6.9 cm

Got questions? Get instant answers now!

Two convex lenses of focal lengths 20 cm and 10 cm are placed 30 cm apart, with the lens with the longer focal length on the right. An object of height 2.0 cm is placed midway between them and observed through each lens from the left and from the right. Describe what you will see, such as where the image(s) will appear, whether they will be upright or inverted and their magnifications.

Got questions? Get instant answers now!

Questions & Answers

what is force
Afework Reply
The different examples for collision
Afework
What is polarization and there are type
Muhammed Reply
Polarization is the process of transforming unpolarized light into polarized light. types of polarization 1. linear polarization. 2. circular polarization. 3. elliptical polarization.
Eze
Describe what you would see when looking at a body whose temperature is increased from 1000 K to 1,000,000 K
Aishwarya Reply
how is tan ninety minus an angle equals to cot an angle?
Niicommey Reply
please I don't understand all about this things going on here
Jeremiah Reply
What is torque?
Matthew Reply
In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study.
Teka
Torque refers to the rotational force. i.e Torque = Force × radius.
Arun
Torque is the rotational equivalent of force . Specifically, it is a force exerted at a distance from an object's axis of rotation. In the same way that a force applied to an object will cause it to move linearly, a torque applied to an object will cause it to rotate around a pivot point.
Teka
Torque is the rotational equivalence of force . So, a net torque will cause an object to rotate with an angular acceleration. Because all rotational motions have an axis of rotation, a torque must be defined about a rotational axis. A torque is a force applied to a point on an object about the axis
Teka
When a missle is shot from one spaceship towards another, it leaves the first at 0.950c and approaches the other at 0.750c. what is the relative velocity of the two shipd
Marifel Reply
how to convert:m^3/s^2 all divided by kg to cm^3/s^2
Thibaza Reply
Is there any proof of existence of luminiferious aether ?
Zero Reply
mass conversion of 58.73kg =mg
Proactive Reply
is Space time fabric real
Godawari Reply
What's the relationship between the work function and the cut off frequency in the diagram above?
frankline Reply
due to the upthrust weight of the object varise with force in which the body fall into the water pendincular with the reflection of light with it
Gift
n=I/r
Gift
can someone explain what is going on here
falanga
so some pretty easy physics questions bring em
falanga
what is meant by fluctuated
Olasukanmi Reply
If n=cv then how v=cn? and if n=c/v then how v=cn?
Natanim
convert feet to metre
Mbah Reply
what is electrolysis
Mbah
Electrolysis is the chemical decomposition of electrolyte either in molten state or solution to conduct electricity
Ayomide
class ninekasindhtextbookurdusave
Ayesha Reply
can someone help explain why v2/c2 is =1/2 Using The Lorentz Transformation For Time Spacecraft S′ is on its way to Alpha Centauri when Spacecraft S passes it at relative speed c /2. The captain of S′ sends a radio signal that lasts 1.2 s according to that ship’s clock. Use the Lorentz transformati
Jennifer
Practice Key Terms 5

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 3' conversation and receive update notifications?

Ask