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F'

parallel rays!

focal point!

focal length f!demo: white board!

converging lens"

horizontal ray goes through focal point behind lens!

converging lens: 3 easy rays"

ray that goes through focal point in front of lens is deflected to be horizontal behind lens!

ray through center of lens is undeflected!

image of an object in a converging lens"

image of an object in a converging lens"

optical axis! optical axis!

image!

converging lens"

f!o!i!

1!o!

1!i!

1!f!+! =!

lens formula!

bb!

converging lens" Derivation of lens equation (1)"

ho!

hi!ho = height of object!

hi = height of image!

f !o-f!

from similar triangles,!

!

hohi

=o " ff

Derivation of lens equation (2)"

ho!

hi!ho = height of object! hi = height of image!

i !

from similar triangles,!

!

ihi

=oho

"hohi

=oi

o !

Derivation of lens equation (3)"

!

hohi

=o " ff

!

oi

=hohi

and!

So,!

!

oi

=o " ff

oi

=of"1

1i

=1f"1o

1i

+1o

=1f Lens equation!

f!o! i!

ho!hi!

f!

magnification"

i!o!hi =! ho!f!

o! i!

ho!hi!

f!

= |M|!i!o!

hi!ho!

=!

magnification M"

|M| < 1!

i!o!

M = -!

i < o!ho! hi!

i!o!

magnification" magnification"

|M| > 1!i > o!i!

ho!hi!

o!

|M| < 1!

i!o!

M = -!

i < o!o!

ho! hi!

i!

f!o = "! i!

1!"!

1!i!

1!f!+! =!

i = f!i!o!

M = - = = 0 !i!"!

magnification"

the image is virtual!!

magnifying lens!

1!o!

1!i!

1!f!+! =!

f!f!o!

i! i < 0 (negative)!

i!o!|M| = > 1 !

converging lens with object distance < focal distance"

converging lens, o > f!

real inverted image!M = -i/o < 0 !

converging lens, o = "!

real image in focal point!M = -i/" = 0!

converging lens, o < f!

virtual upright image!M = -i/o > 1 !

M < 0!! ! !|M| > 1 !

BUT: possible! !|M| < 1!{!

summary: converging lens" example problem: projector"

You set up a projector so that it is in focus, but the image is too small, and you move the projector farther from the screen. !

1. Is the lens in the projector a converging lens or a diverging lens?!

example problem: projector"

You set up a projector so that it is in focus, but the image is too small, and you move the projector farther from the screen. !

1. Is the lens in the projector a converging lens or a diverging lens?!

A converging lens. Any lens that makes a real image that can be seen on a screen is a converging lens.!

example problem: projector"

You set up a slide projector so that it is in focus, but the image is too small, and you move the projector farther from the screen. !

1.  Is the lens in the projector a converging lens or a diverging lens?!

2.  After you move the projector back, to focus the image again do you move the slide closer to or farther from the focal point of the lens?!

example problem: projector"

You set up a slide projector so that it is in focus, but the image is too small, and you move the projector farther from the screen. !

1.  Is the lens in the projector a converging lens or a diverging lens?!

2.  After you move the projector back, to focus the image again do you move the slide closer to or farther from the focal point of the lens?!

!Closer to the focal point!

A converging lens. Any lens that makes a real image that can be seen on a screen is a converging lens.!

f = 10 cm!i=?!

1. !o = 20 cm!

2. !Object farther away!!o = 50 cm!!o " "!

3. !Object closer than f!!o = 4 cm!

bb!

example problem: converging lens"

f = 10 cm!i=?!

1. !o = 20 cm ! ! ! !i = 20 cm! !M = 1!

2. !Object farther away! ! !!!o = 50 cm ! ! ! !i = 12.5 cm !M = 0.25!!o " " ! ! ! ! !i " f ! !M " 0!

3. !Object closer than f!!o = 4 cm ! ! ! !i = -6.7 cm !M = 1.7!

example problem: converging lens"

!

1o

+1i

=1f

A nice applet for understanding converging lenses:"

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=48!

Images Formed by Converging Lens "

•  Object (O) is in front of F1 : real, inverted, enlarged or reduced !

#  Object (O) in between F1 and lens: virtual, upright, enlarged.!

f > 01i+1o=1f

M =hiho= !

io

f > 01i+1o=1f

M =hiho= !

io

25!

f < 0!

i < 0#virtual image #

for any o!

1!o!

1!i!

1!f! -!=!

diverging lens"

bb: 3 easy rays!

diverging lens: 3 easy rays"horizontal ray is deflected so that it extrapolates back to focal point in front of lens!

ray that goes through center of lens — this ray is undeflected!

ray from object to focal point in back of lens is deflected so that it is horizontal!

bb2: 3 easy rays!

diverging lens"

diverging lens" diverging lens"

diverging lens" diverging lens"

virtual upright image!

diverging lens" diverging lens: object at infinity"

image in focal point!

diverging lens: object at infinity" diverging lens: o < f"

diverging lens: o < f" diverging lens: o < f"

diverging lens: o < f"

virtual upright image!

diverging lens: o < f"

diverging lens"

image is #!virtual#!right-side-up#!in front of lens!

Images Formed by Diverging Lenses"

Images are always virtual, upright, and reduced !Images are always virtual, upright, and reduced !

f < 01o+1i=1f

M =hiho= !

io

42!

Summary of sign conventions"

>0 <0 f concave mirrors

converging lens convex mirrors diverging lens

o object side the other side i real virtual

M=-i/o upright inverted

Real Virtual mirrors front behind lenses behind font

43!

Converging and Diverging Lenses"

sign convention:!f<0!

sign convention:!f>0!

44!

Combination of Lenses"

!

M = M1M2

45!

Cameras "•  A camera is essentially a converging lens with a short

focal length. (Operating condition: o>>f ! i ~ f) !

46!i o

Eyes"•  The eye is essentially an auto-focus camera!

Quick quiz: Is the image on retina real/virtual, ! upright/inverted?!

Psychological size!(image size on retinal) !is determined by !"

47!

Simple Magnifier"•  A simple magnifier is essentially also a converging

lens with a short focal length. !–  Operating condition: o<f and i~-25 cm!–  Simple magnifiers magnify the opening angle an object

subtends at the eye (i.e. psychological size) !

angular magnification:!m = #/#0 ! = 25cm/f for near point!

48!

Compound Microscopes (cont)"

Robert Hooke’s Microscope!(1665)!

49!

Compound Microscope"•  Compound microscope also does angular magnification.!

•  Configuration: L >> fe+fo !

Mo~L/fo!Me=25 cm/fe!M=MoMe!

= (L/fo) (25 cm/fe)!Final Image: Virtual, inverted 50!

Telescopes (cont)"

Galileo’s Telescope!

51!

Telescopes"•  Telescope is another type of angular

magnification device with configuration L ~fe+fo !

Mo= fo/fe!

Note: For telescope application, object distance can not be adjusted. 52!