Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Lecture 25

Chapter 23

Ray Optics

Thin Lenses

Course website:http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsII

Lecture Capture: http://echo360.uml.edu/danylov201415/physics2spring.html

04.28.2015Physics II

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Focusing effect

The light pattern at the bottom of a swimming pool on a sunny day consists of bright lines.

Water waves focus light.The same focusing effect is used in lenses.

The same effect is used in lenses to focus light

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

There are two types of lensesA converging lens causes the rays to refract toward the optical axis.

A diverging lens refracts parallel rays away from the optical axis

converging lens

R1

R2

diverging lens

R1

R2

How can they be made?

A converging lens is thicker in the center than at the edges.

A diverging lens is thicker atthe edges than in the center.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Lensmaker’s EquationThis useful equation relates the radii of curvature of the two lens surfaces, and the index of refraction, to the focal length:

11

1 1

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Converging Lens

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

A ray initially parallel to the optic axis will go through the far focal point after passing through the lens.

A ray through the near focal point of a thin lens becomes parallel to the optic axis after passing through the lens.

There are three typical situations which are used in Ray Tracing for a converging lens:

A ray through the center of a thin lens is neither bent nor displaced but travels in a straight line.

Ray 1 Ray 2 Ray 3

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Converging lens. Real Image

Near focal point

Farfocal point

Object

Image

1

23

Lens planeObject plane

Image plane

Optical axis F1

F2O

Object distance Image distanceS S’(inverted real image)

P

RR’

P’

Note!!! For a converging lens f is positive f > 0

f f (focal length)

If after using the lens equation, s’ is positive Image is realIf after using the lens equation, s’ is negative Image is virtual

h

h'

and S > 0 is positive all the time s> 0

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Examples of real inverted images

A lens produces a sharply focused, inverted image on a screen. What will you see on the screen if a piece of dark paper is lowered to cover the top half of the lens?top half of the lens?

ConcepTest 1 Half-blocked lens.

Image

1

23

F1

F2O

(inverted image)

A. An inverted but blurry image.B. An image that is dimmer but

otherwise unchanged.C. Only the top half of the image.D. Only the bottom half of the image.E. No image at all.

screen

Still the same image but it is created by less number of rays

A lens produces a sharply focused, inverted image on a screen. What will you see on the screen if the lens is covered by a dark mask having only a small hole in the center?half of the lens?

ConcepTest 2 Half-blocked lens.

Image

1

23

F1

F2O

(inverted image)

A. An inverted but blurry image.B. An image that is dimmer but

otherwise unchanged.C. Only the top half of the image.D. Only the bottom half of the image.E. No image at all.

screen

Still the same image but it is created by less number of rays

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

MagnificationThe image can be either larger or smaller than the object,

depending on the location and focal length of the lens.

The lateral magnification m is defined as:

A positive value of m indicates that the image is upright relative to the object.A negative value of m indicates that the image is inverted relative to the object.

Δ′ ′ ′

(inverted image) Δ

The minus is introduced so that:

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Converging lens. Virtual Image

ObjectImage

1

2

3 Optical axis

F1

F2O

Object distanceImage distance

S

S’

(virtual imagein upright position)

For a converging lens f > 0

f

After using the lens equation, s’ must be negative Image is virtual

hh'

The image distance S' for a virtual image is defined to be a negative number S'<0).

Consider a converging lens for which the object is inside the focal point, at distance s < f.

You can see all three rays appear to diverge from point P.Image is an upright and virtual.

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Virtual Magnified Images You can “see” a virtual image by

looking through the lens. This is exactly what you do with a

magnifying glass, microscope or binoculars.

Slide 23-111

Doc uses a magnifying glass in 1955 to read the letter written by his 1985 counterpart.

A lens creates an image as shown. In this situation, the object distance s is

ConcepTest 3 Converging lensA. Larger than the focal length f.B. Equal to the focal length f.C. Smaller than focal length f.

The image is inverted and real. It is only possible when s > f s > f

s < f

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Diverging Lens

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

There are three typical situations which are used in Ray Tracing for a diverging lens:

Ray 1

Ray 2

Ray 3

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Optical axis

F1 F2

SS’

(virtual imagein upright position)

h

h'

f

O

Let’s find an image distance s’ using the lens equation

Note!!! For a diverging lens f is negative f < 0 and S > 0 is positive all the time

Solve for s’ 100 ∙ 50100 50

33.3s’ is negative, soImage is virtual

(And we got the same answer graphically)Let’s find magnification using.

.A positive value of m indicates that the image is upright relative to the object.

Consider a diverging lens for which the object is outside the focal point, at distance s > f.You can see all three rays appear to diverge from point P.Point P is an upright, virtual image of the object point P.

Light rays are converging to point 1. The lens is inserted into the rays with its focal point at point 1. Which picture shows the rays leaving the lens?

ConcepTest 4 Diverging lens

Ray 2

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

The sign conventions

Focal length, f f > 0 for a converging lens

f < 0 for a diverging lens

Image distance, s’ s’ > 0, for a real image

s’ < 0, for a virtual image

Magnification, m m > 0, for an upright image

m < 0, for an inverted image

Object distance, s s > 0 s > 0

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

What you should readChapter 23 (Knight)

Sections 23.4 and 23.5 skip them 23.6

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Thank youSee you on Friday

Department of Physics and Applied Physics95.144, Spring 2015, Lecture 25

Types of lenses

The power of a lens is the inverse of its focal length:

Lens power is measured in diopters, D:

1 D = 1 m-1.