1 From Last Time… Lenses and image formation Object Image Lens Object Image Thurs. Sep. 17, 2009Physics 208, Lecture 5.

1

From Last Time…

Lenses and image formation

Object

Image

Lens

Object

Image

Thurs. Sep. 17, 2009 Physics 208, Lecture 5

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 2

1) Rays parallel to optical axis pass through focal point.2) Rays through center of lens are not refracted.

3) Rays through F emerge parallel to optical axis.

Thin-lens approximation: Ray tracing

F

F

Object

ImageOptical Axis

Here image is real, inverted, enlarged

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 3

Making an image

s’s

Object Image

Image distanceObject distance

f f

focal length

How are all these related?

€

1

s+

1′ s

=1

f

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 4

QuestionA magnifying glass of diameter 2 cm and focal

length 5 cm is used to form an image of the sun. Approximately what is the image distance?

A. 0.2 cm

B. 1 cm

C. 2 cm

D. 2.5 cm

E. 5 cm

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 5

Image size vs object size: Magnification

= M = Magnification

€

image height

object height=

′ s

s=

image distance

object distance

Image height

Image distance

Objectdist.

Objectheight

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 6

Far away objectsThe moon is 3.8x108 m away, and 3.5x106 m diameter. I use a

1 m focal length lens to make an image of the moon. About what diameter is this image of the moon?

A. 0.5 cm

B. 1 cm

C. 2 cm

D. 10 cm

E. 1 m

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 7

Different object positions

Image (real, inverted)

Image (real, inverted)Object

Image (virtual, upright)

These rays seem to originatefrom tip of a ‘virtual’ arrow.

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 8

Virtual images

Virtual image can’t be recorded on film, Can’t be seen on a screen.

But rays can be focused by another lens e.g. lens in your eye (focus on retina) e.g. lens in a camera (focus on film plane)

Image (virtual, upright)

These rays seem to originatefrom tip of a ‘virtual’ arrow.

objects closer to a converging lens than the focal length form a virtual image

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 9

Do these rays come from real image, a virtual image, or an object?

Can’t tell. Rays are exactly equivalent, and can be imaged by a lens in exactly the same way.

Virtual Image : thin-lens equation

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 10

Image (virtual)

Object

Object distance sFocal length f ( >0 for converging lens )Image distance s’

€

1

s+

1′ s

=1

f

€

⇒1′ s

=1

f−

1

sObject distance < focal length

€

s < f ⇒ ′ s is negative

Negative image distance: image on same side as object

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 11

Object at near point –

biggest it can appear when in focus

Magnifying glass

o

• Object closer than focal point

—Lens produces virtual image

• Light rays appear to originate from virtual image

• Virtual image is used as object for eye lens.

• Have moved object ‘closer’, while permitting eye to focus

Image (virtual, upright)

ss’

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 12

Magnifying glassA magnifying glass has a focal length of 8 cm.

It is 1 cm in front of your eye.

What is the closest that you can hold it to a bug so that the bug is in focus (your eye has a near point of 25cm).

A. 4 cm

B. 6 cm

C. 8 cm

D. 12 cm

E. 25 cm

€

1

s=

1

f−

1′ s

1

s=

1

8cm−

1

−24cm=

3

24cm+

1

24cm=

1

6cm

1cm

s=?

Magnifying glass: angular magnification

Without magnifying glass, object is biggest at near point, ~ 25 cm. Subtends angle

With magnifier Object can be closer, at object distance s Subtends angle

Angular magnification is Increases with decreasing obj. dist. Smallest obj. dist. is for image at near point:

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 13

€

NP ~ h /25cm

€

1

s=

1

f−

1

−25cm€

mag ~ h /s

€

M = θmag /θNP = 25cm /s

€

Mmax = θmag /θNP = 25cm1

f+

1

25cm

⎛

⎝ ⎜

⎞

⎠ ⎟=

25cm

f+1

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 14

Diverging lens

OpticalAxis

Then thin-lens equation can be used:

€

1

s+

1′ s

=1

f

Object Image

Focal length defined to be negative

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 15

Virtual image and diverging lens

Example: object at infinity Rays appear to originate from

focal point. Result

Object has been (virtually) transported to a new location

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 16

Object

Nearsightedness

I can’t focus on this

This, I can see

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 17

Object

Fixing nearsightedness

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 18

Reading glasses

Without my glasses, my far point is about 25 cm. What is the weakest (longest focal length) corrective lens (located at my eye) would let me read a newspaper holding it 50 cm away?

A. -25 cm

B. +25 cm

C. -50 cm

D. +50 cm

E. -100 cm

F. +100 cm

Lens should form a virtual image closer to my eye.

I can focus on image only if it is less than 25 cm away.Weakest lens moves it least, so image distance = -25 cm.

€

1

f=

1

50cm+

1

−25cm=

1

50cm−

2

50cm=

1

−50cm

Diopters Two lenses close together ~

Single lens, “effective” focal length feff

Lens power P Defined as with f in meters Units of P are diopters Two lenses close together

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 19

€

1

feff

=1

f1

+1

f2

€

P =1/ f

€

Peff = P1 + P2

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 20

Far away objectsThe moon is 3.8x108 m away, and 3.5x106 m diameter. I use a

1 m focal length lens to make an image of the moon. About what diameter is this image of the moon?

A. 0.5 cm

B. 1 cm

C. 2 cm

D. 10 cm

E. 1 m

Not a very big image. How can It be made ‘bigger’?

Look at the image with a magnifying glass!

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 21

Telescope: two lenses, object far away

Eyepiece forms virtual image Real image formed on retina by your eye lens.

Objective: Forms real image of far-away objectEyepiece: Used as magnifying glass to examine image

EyepieceObjective

Telescope angular magnification Without telescope,

distant planet subtends angle

Objective lens forms real image Height Used as object by eyepiece lens

Eyepiece Forms virtual image at infinity (for relaxed eye) Object must be at focal point Subtends angle

Angular mag: Thurs. Sep. 17, 2009 Physics 208, Lecture 5 22

€

planet

€

himageobj = fobjθ planet

€

image = himageobj / feyepiece

€

image /θ planet = fobj / feyepiece

Thurs. Sep. 17, 2009 Physics 208, Lecture 5 23

Virtual image ‘Object’

Eyepiece

Compound Microscope

qp

Object

Real, inverted, image

Objective

Object outside focal pointForms a real image

Real image used as object for eyepiece.Eyepiece forms virtual image for eye.