How well do you know Lenses? Lenses work because of A. refraction B. reflection c. Both

Lenses refract light! Converging Lenses (a) are thicker in the middle Diverging Lenses (b) are thinner

How are mirrors like Lenses? A concave lens acts much like: a. concave mirrorb. convex mirror c. flat mirrord. convex lens

1. refract not reflect 2. behave opposite of mirrors (concave mirror= convex lens) 3. assume thin so easy geometry 4. brighter than mirrors (no light loss to absorption) 5. less perfect than mirrors (lens sensitive to color & angle)

Lens Aberrations Spherical & chromatic Astigmatism Coma

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? A. top-focuses b. bottom-defocuses which lens is converging? A. top-focuses b. bottom-defocuses

Focal length: f = + for convex, f= - for concave f = +5 cm f = -5 cm f f f f Sign Conventions for Lenses Object distance: d o = + for objects on left side Image distance: d i = + for real images on left side = - for virtual images on right side

Converging and Diverging Lenses 3 Principle Rays 3 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 f C 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 f C C

f f Practice Ray Tracing!

Convex Lens: Principal Ray#2 (from focus, through lens parallel) f f C C

f f Practice Ray Tracing!

Convex Lens:Principal Ray#3 (no change through lens middle) f f C C

f f Practice Ray Tracing!

3 unique locations to place at object 1. further than focal point (d > f) 2. At 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? a. 1 b. 2 c. -1 d. -2 e. 0 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

f f

Concave Lens: Principal Ray#2 (aim for far focal point, hit lens, then emerge parallel out) f f

f f

Concave Lens: Principal Ray#3 (no changed through middle of lens) f f

What type image do concave lenses (convex mirrors) always make? A. real, small B. virtual, big C. real, bigD. virtual, small

f ff f Which lens can produce a virtual, upright, large image? A. concaveb. convexc. bothd. neither

f ff f Which lens can produce a real, upright, large image? A. concaveb. convexc. bothd. neither

f ff f How can you create a real, inverted, large image? A. concave- object between f and lens B. concave- object between f and 2f (C) C. concave- object past the center (C) D. convex- object placed anywhere

f f

FYI: Multiple Lenses The real image of one lens becomes the object for the next image! Why need to know this? compound lenses are found in cameras, telescopes, compound lenses are found in cameras, telescopes,

FYI: Camera Lens sold based on lowest f-number I= Intensity is 4x stronger if f-number is 2x as low (price 4x higher too!)

FYI: The Eye The camera is modeled after the eye “Normal” reading distance is 25 cm Eye is about 2.5 cm in diameter Most of focusing is done by the cornea and vitreous humor behind the cornea

Myopia: near sighted (can’t see far) Contacts diverges light so not so focused

Hyperopia: far sighted (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 fofo fofo Object Image fefe 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 fofo fofo fefe 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 fofo fofo fefe fefe 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 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 of objective and eyepieceLength of telescope light path is sum of focal lengths of objective and eyepiece

FYI: Compound Microscope Magnification is product of lateral magnification of objective and angular magnification of eyepieceMagnification is product of lateral magnification of objective and angular magnification of eyepiece Note: Image is viewed at infinityNote: Image is viewed at infinity

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 fefe fefe Object fofo fofo Eye Image Objective Lens Eyepiece 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 fefe fefe Object fofo fofo Eye Final Magnified Image