Thin LensesThin Lenses

Chapter 15Chapter 15

What is a lens?What is a lens?

A transparent object that refracts A transparent object that refracts light rays, causing them to light rays, causing them to converge or diverge to create an converge or diverge to create an imageimage

Converging LensesConverging Lenses

A converging lens is thicker at the A converging lens is thicker at the middle than it is at the rimmiddle than it is at the rim– The front of the lens is the side of The front of the lens is the side of

the lens where the object isthe lens where the object is

Converging lenses can produce Converging lenses can produce real or virtual imagesreal or virtual images

Converging LensesConverging Lenses

The focal points are equidistant from the center of the lens. That distanceis the focal length of the lens.

F F 2 F2 F

Converging Lens Converging Lens Reference Rays Reference Rays (p.569)(p.569)

RayRay From object From object to lensto lens

From lens to From lens to imageimage

Parallel RayParallel Ray Parallel to Parallel to principal axisprincipal axis

Passes Passes through focal through focal point Fpoint F

Central RayCentral Ray To the center To the center of the lensof the lens

From the From the center of the center of the lenslens

Focal rayFocal ray Passes Passes through focal through focal point Fpoint F

Parallel to Parallel to principal axisprincipal axis

Converging LensesConverging Lenses

The focal points are equidistant from the center of the lens. That distanceis the focal length of the lens.

F F 2 F2 F

Ray 1

Ray 2

Ray 3

Images Created by Converging Lenses Images Created by Converging Lenses (p.571)(p.571)

Images produced by lenses Images produced by lenses (p. 570-571)(p. 570-571)

An object An object infinitely far infinitely far away from a away from a converging lens converging lens will create a will create a point image at point image at the focal pointthe focal point– i.e. light from i.e. light from

the Sunthe Sun

Images produced by lenses Images produced by lenses (p. 570-571)(p. 570-571)

As a distant object As a distant object approaches the focal approaches the focal point, the image point, the image becomes larger and becomes larger and farther awayfarther away

Images produced by lenses Images produced by lenses (p. 570-571)(p. 570-571)

When the When the object is at the object is at the focal point, the focal point, the light rays exit light rays exit parallel to each parallel to each other and the other and the image is “at image is “at infinity”infinity”– i.e. a lighthouse i.e. a lighthouse

or a searchlightor a searchlight

Images produced by lenses Images produced by lenses (p. 570-571)(p. 570-571)

When the object is inside the When the object is inside the focal point, the rays are drawn focal point, the rays are drawn the same way but you must the same way but you must extend them backwards in order extend them backwards in order to find the imageto find the image

Converging Lens: Objects inside the Converging Lens: Objects inside the focal pointfocal point

F F 2 F2 F

These rays are diverging and won’t cross

Draw lines extending backwards to form the image

Thin Lens and Thin Lens and Magnification Equations Magnification Equations (p.574)(p.574)

fqp

111

p

qM

Sign conventions for Sign conventions for lenses p.574lenses p.574

++

pp Object distance for Object distance for lenseslenses

qq Image in back of Image in back of the lensthe lens

Image in front Image in front of the lensof the lens

ff Converging LensConverging Lens Diverging LensDiverging Lens

Sample Problem p.576 Sample Problem p.576 #2#2 Sherlock Holmes examines a clue Sherlock Holmes examines a clue

by holding his magnifying class by holding his magnifying class (with a focal length of 15.0 cm) (with a focal length of 15.0 cm) 10.cm away from an object. Find 10.cm away from an object. Find the image distance and the the image distance and the magnification. Describe the magnification. Describe the image he observes. Draw a ray image he observes. Draw a ray diagram to confirm your answers.diagram to confirm your answers.

What kind of lens is a What kind of lens is a magnifying glass?magnifying glass?

Magnifying glasses produce Magnifying glasses produce enlarged images. Therefore, a enlarged images. Therefore, a magnifying glass is a converging magnifying glass is a converging lens. lens.

f = + 15 cm, p= +10 cmf = + 15 cm, p= +10 cm

Solve the problemSolve the problem

30

1

10

1

15

1111

pfq cm 30q

310

30

cm

cm

p

qM

The image is virtual and upright

Magnifying Lens Ray DiagramMagnifying Lens Ray Diagram

F F 2 F2 FObject

Notice that the image is located at 2F (30 cm) and it is also in front of the lens which is why q is negative.

Diverging LensesDiverging Lenses

A diverging lens is thinner at the A diverging lens is thinner at the middle than it is at the rimmiddle than it is at the rim

A diverging lens has two focal A diverging lens has two focal points but only one focal lengthpoints but only one focal length

Diverging lenses only produce Diverging lenses only produce virtual imagesvirtual images

Diverging LensesDiverging Lenses

The focal points are equidistant from the center of the lens. That distanceis the focal length of the lens.

F F 2 F2 F

Diverging Lens Reference Rays (p.569)Diverging Lens Reference Rays (p.569)

RayRay From object From object to lensto lens

From lens to From lens to imageimage

Parallel RayParallel Ray Parallel to Parallel to principal axisprincipal axis

Directed away Directed away from focal from focal point Fpoint F

Central RayCentral Ray To the center To the center of the lensof the lens

From the From the center of the center of the lenslens

Focal rayFocal ray Proceeding Proceeding toward back toward back focal point, Ffocal point, F

Parallel to Parallel to principal axisprincipal axis

Drawing the RaysDrawing the Rays

F F 2 F2 F

Ray 1

Ray 2

Ray 3

Sample Problem (p.579 Sample Problem (p.579 #1)#1)

Using a ray diagram, find the Using a ray diagram, find the position and height of an image position and height of an image produced by a viewfinder in a produced by a viewfinder in a camera with a focal length of 5.0 camera with a focal length of 5.0 cm if the object is 1.0 cm tall and cm if the object is 1.0 cm tall and 10.0 cm in front of the lens. A 10.0 cm in front of the lens. A camera viewfinder is a diverging camera viewfinder is a diverging lens.lens.

Ray DiagramRay Diagram

F F 2 F2 F

Object

The image is about 1/3 of the object height (.33 cm). The image location is about 3 or 4 cm from the lens. So, q is approximately -3.5 cm.

Smart people verify!Smart people verify!

10

3

10

1

5

1111

pfqcmq 3.3

p

q

h

hM

o

i

cmcm

cmcm

p

qhh oi 33.

10

)33.3(1)(