!"#$%&$'()(*'+,&-./,'(0' focal point! parallel rays! converging lens" image of an object in a converging lens" converging lens: 3 easy rays" !

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1 !"#$%&$'()(*'+,&-./,'(0' converging lens"! +,7$,$'! 8,9/4&:27'473'+,7$,$'! 84#';%4</4=$'! +,7$'>?.4:27' 1",'A.=47'>#,*'+,7$,$'473'B4<7%C,/$' B%&/2$&26,$''! 1,E,$&26,$' parallel rays! focal length f! focal point! demo: white board! converging lens: 3 easy rays" image of an object in a converging lens" horizontal ray goes through focal point behind lens! ray through center of lens is undeflected! ray that goes through focal point in front of lens is deflected to be horizontal behind lens!

2 image of an object in a converging lens" converging lens" optical axis! optical axis! image! converging lens" Derivation of lens equation (1)" f! 1! 1! +! 1! =! f! lens formula! o-f! h o! h o = height of object! from similar triangles,! f! h i! h i = height of image! bb! h o h i = o " f f

3 Derivation of lens equation (2)" Derivation of lens equation (3)" h o! o! i! h o h i = o " f f and! o i = h o h i h o = height of object! from similar triangles,! i = o h i h o " h o h i = o i h i! h i = height of image! So,! o = o " f i f o = o i f "1 1 i = 1 f " 1 o 1 i + 1 o = 1 f Lens equation! magnification" magnification M" h h h h f! f! f! f! h i! h =! h i =! h = M!

4 magnification" M = -! magnification" M = -! h h h h i < o! M < 1! i < o! M < 1! h h i > o! M > 1! o = "! magnification" f! 1! 1! +! =! "! i = f! 1! f! M = - = = 0! "! converging lens with object distance < focal distance" f! f! 1! 1! +! 1! =! f! i < 0 (negative)! the image is virtual!! M = > 1! magnifying lens!

5 summary: converging lens" example problem: projector" converging lens, o = "! converging lens, o > f! converging lens, o < f! 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?! real image in focal point! M = -i/" = 0! real inverted image! M = -i/o < 0! virtual upright image! M = -i/o > 1! M < 0!! {!!! M > 1! BUT: possible!! M < 1! example problem: projector" 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.! 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?! 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.! 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?!

6 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?! A converging lens. Any lens that makes a real image that can be seen on a screen is a converging 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! f = 10 cm! i=?! example problem: converging lens" 1.!o = 20 cm! 2.!Object farther away!!o = 50 cm!!o " "! 3.!Object closer than f!!o = 4 cm! bb! f = 10 cm! i=?! example problem: converging lens" 1 o + 1 i = 1 f 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! A nice applet for understanding converging lenses:" 3.!Object closer than f!!o = 4 cm!!!!i = -6.7 cm!m = 1.7!

7 Images Formed by Converging Lens " f > 0 1 i + 1 o = 1 f M = h i h o =! i o Object (O) is in front of F 1 : real, inverted, enlarged or reduced! diverging lens" 1! f < 0! =! 1! f! -! 1! f > 0 1 i + 1 o = 1 f M = h i h o =! i o i < 0# virtual image # for any # Object (O) in between F 1 and lens: virtual, upright, enlarged.! 25! diverging lens: 3 easy rays" horizontal ray is deflected so that it extrapolates back to focal point in front of lens! diverging lens" ray from object to focal point in back of lens is deflected so that it is horizontal! ray that goes through center of lens this ray is undeflected! bb: 3 easy rays! bb2: 3 easy rays!

8 diverging lens" diverging lens" diverging lens" diverging lens"

9 diverging lens" diverging lens: object at infinity" virtual upright image! diverging lens: object at infinity" diverging lens: o < f" image in focal point!

10 diverging lens: o < f" diverging lens: o < f" diverging lens: o < f" diverging lens: o < f" virtual upright image!

11 diverging lens" Images Formed by Diverging Lenses" f < 0 1 o + 1 i = 1 f M = h i h o =! i o image is#!virtual#!right-side-up#!in front of lens! Images are always virtual, upright, and reduced! Images are always virtual, upright, and reduced! 42! Summary of sign conventions" Converging and Diverging Lenses" >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 sign convention:! f>0! Real Virtual mirrors front behind lenses behind font 43! 44! sign convention:! f<0!

12 M = M 1 M 2 Combination of Lenses" Cameras " A camera is essentially a converging lens with a short focal length. (Operating condition: o>>f! i ~ f)! 45! o 46! i Eyes" The eye is essentially an auto-focus camera! Psychological size! (image size on retinal)! is determined by!" 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! Quick quiz: Is the image on retina real/virtual,! upright/inverted?! 47! 48!

13 Compound Microscopes (cont)" Robert Hooke s Microscope! (1665)! Compound Microscope" Compound microscope also does angular magnification.! Configuration: L >> f e +f o! 49! Final Image: Virtual, inverted 50! M o ~L/f M e =25 cm/f e! M=M o M e! = (L/f o ) (25 cm/f e )! Telescopes (cont)" Telescopes" Telescope is another type of angular magnification device with configuration L ~f e +f o! Galileo s Telescope! 51! M o = f o /f e! 52! Note: For telescope application, object distance can not be adjusted.

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