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