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How well do you know Lenses?
Lenses work because of
• A. refraction B. reflection c. Both
Lenses refract light!Lenses refract light!Converging Lenses (a) are thicker in the middleConverging Lenses (a) are thicker in the middle
Diverging Lenses (b) are thinner Diverging Lenses (b) are thinner
How are mirrors like Lenses?
A concave lens acts much like:a. concave mirror b. convex mirrorc. flat mirror d. convex lens
1. refract not reflect1. refract not reflect
2. behave opposite of mirrors2. behave opposite of mirrors(concave mirror= convex lens)(concave mirror= convex lens)
3. assume thin so easy geometry3. assume thin so easy geometry
44. brighter than mirrors. brighter than mirrors(no light loss to absorption)(no light loss to absorption)
5. less perfect than mirrors5. less perfect than mirrors(lens sensitive to color & angle)(lens sensitive to color & angle)
Lens AberrationsLens Aberrations
Spherical & chromaticSpherical & chromatic AstigmatismAstigmatism ComaComa
C f
Principal Axis
Center of Curvature
focus
Note: f = C/2
The Center of Curvature is equal to the radius of the circle formed by the lens
vertex
Lens Terminology
which lens is converging?which lens is converging?A. top-focuses b. bottom-defocusesA. top-focuses b. bottom-defocuses
Focal length: f = + for convex, f= - for concave
f = +5 cm
f = -5 cmf f f f
Sign Conventions for Lenses
Object distance: do = + for objects on left side
Image distance: di = + for real images on left side = - for virtual images on right side
Converging and Diverging LensesConverging and Diverging Lenses
3 Principle Rays3 Principle Rays
a positive lens (f=+) is also called
a. converging b. convex c. diverging d. concave e. both a & b f. both c & d
f fC C
f = C/2
Negative Lens (f=-): also called concave or diverging
f = C/2
f f
Convex Lenses:Principal Ray#1(parallel, then opposite focal point)
f fC C
f f
Practice Ray Tracing!
Convex Lens: Principal Ray#2(from focus, through lens parallel)
f fC C
f f
Practice Ray Tracing!
Convex Lens:Principal Ray#3(no change through lens middle)
f fC C
f f
Practice Ray Tracing!
3 unique locations to place at object3 unique locations to place at object
1. further than focal point (d > f)1. further than focal point (d > f)
2. At focal point (d=f)2. At focal point (d=f)
3. Less than focal point (d < f)3. Less than focal point (d < f)
What is the magnification of an object placed at the center of a convex lens?What is the magnification of an object placed at the center of a convex lens?
a. 1 a. 1 b. 2 b. 2 c. -1 c. -1 d. -2 d. -2 e. 0e. 0
Magnification = -1 (same size, but inverted. Real too!)Magnification = -1 (same size, but inverted. Real too!)
What type of image comes from placing an object far from a convex lens?A. real, inverted B. real, upright
C. virtual, upright D. virtual, inverted
What type of image comes from placing an object far from a convex lens?A. real, inverted B. real, upright
C. virtual, upright D. virtual, inverted
What happens to the image as the object (candle) is placed closer to the lens?
A. bigger B. smaller C. same
Which case for placing an object would create a real image?
A. 1 B. 2 C. 1, 2, 3 d. 4
Concave Lens: Principal Ray#1(parallel, diverge as if from focal point
f f
ff
Concave Lens: Principal Ray#2(aim for far focal point, hit lens, then emerge parallel out)
f f
ff
Concave Lens: Principal Ray#3(no changed through middle of lens)
f f
What type image do concave lenses What type image do concave lenses (convex mirrors) always make?(convex mirrors) always make?
A. real, small A. real, small B. virtual, bigB. virtual, bigC. real, bigC. real, big D. virtual, smallD. virtual, small
fff f
Which lens can produce a virtual, upright, large image?
A. concave b. convex c. both d. neither
fff f
Which lens can produce a real, upright, large image?
A. concave b. convex c. both d. neither
ff f f
How can you create a real, inverted, large image?
A. concave- object between f and lensB. concave- object between f and 2f (C)C. concave- object past the center (C)D. convex- object placed anywhere
ff
FYI: Multiple LensesFYI: Multiple LensesThe real image of one lens becomes the The real image of one lens becomes the
object for the next image!object for the next image!
Why need to know this?Why need to know this?
compound lenses are found in cameras, compound lenses are found in cameras, telescopes, telescopes,
FYI: CameraFYI: CameraLens sold based on Lens sold based on
lowest f-numberlowest f-number
I= Intensity is 4x I= Intensity is 4x stronger if f-number is stronger if f-number is 2x as low2x as low
(price 4x higher too!)(price 4x higher too!)
Df
numberf
22 numberf
1
Df
1I
FYI: The EyeFYI: The EyeThe camera is modeled after the eyeThe camera is modeled after the eye
““Normal” reading distance is 25 cmNormal” reading distance is 25 cm
Eye is about 2.5 cm in diameterEye is about 2.5 cm in diameter
Most of focusing is done by the cornea and vitreous Most of focusing is done by the cornea and vitreous humor behind the corneahumor behind the cornea
Myopia: near sighted Myopia: near sighted (can’t see far)(can’t see far)
Contacts diverges light so not so focusedContacts diverges light so not so focused
metersf1
DioptersP
Hyperopia: far sightedHyperopia: far sighted(can’t see near)(can’t see near)Reading glasses- convex lens adds focus
FYI: Telescopes: astronomical is most powerful, but stars upside down !
•Astronomical Telescope-
•2 converging lenses (objective, eyepiece)•Image is inverted, virtual, magnified
•Terrestial (Galilean Telescope)-
•1 converging lens & 1 diverging lens•Image is upright, virtual, magnified
Astronomical Telescope
fo fo
Object
Image
fefe
• Note the image from the objective lens is inverted• The image is inside the focal point of the
eyepiece (for magnification)
Eye
Astronomical Telescope
fo fo
fefe
• The image from the objective lens is treated as an object for the eyepiece
• Note that since it is inside the focal point of the eyepiece the final image is magnified
Eye
Final Image
Terrestrial Telescope
Eyepiece
Objective Lens
fo fofe fe
Eye
• Note that the eyepiece is located inside the focal point of the objective lens
• The diverging eyepiece lens intercepts the rays of light from the objective lens before the image can be inverted & magnifies the final image
FYI: Astronomical TelescopeFYI: Astronomical Telescope• Object is at infinity so image is at fObject is at infinity so image is at f• Measure angular magnificationMeasure angular magnification• Length of telescope light path is sum of focal lengths Length of telescope light path is sum of focal lengths
of objective and eyepieceof objective and eyepiece
e
o
ff
m
FYI: Compound MicroscopeFYI: Compound Microscope
• Magnification is product of Magnification is product of lateral magnification of lateral magnification of objective and angular objective and angular magnification of eyepiecemagnification of eyepiece
• Note: Image is viewed at Note: Image is viewed at infinityinfinity
eoeo f
cm25fL
mMM
Compound Microscope
• Note that the compound micrscope is similar to an astronomical telescope backwards
• The objective lens forms a real, enlarged, inverted image inside the focal point of the eyepiece
fe fe Objectfofo
Eye
Image
Objective LensEyepiece Lens
Compound Microscope
• The objective lens forms a real, enlarged, inverted image inside the focal point of the eyepiece
• The first image is further magnified by the eyepiece--thus the term compound
fe fe
Object
fofo
Eye
Final Magnified Image
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