Physics 1230 Light and Color http://www.colorado.edu/physics/phys1230/ phys1230_sm15/ Dr. Ka'e Hinko kathleen.hinko@colorado.edu Office: JILA A502
Agenda, Day 11: Ques'ons and Paper Topic (5 min) Finish Module 4 Prac'ce Ray Tracing (10 min) Wrap up (10 min) Start Module 5 Cameras (30 min) Eyes (30 min) RE #4 is due right now HW #5 is due tomorrow
10 Class Modules Each equal to about one week in regular term 1. How does light travel? 2. How do we see things that don t emit light? 3. Does light always travel in a straight line? 4. How do lenses make things look different than they are? 5. How does our eye see light? 6. How does our brain process light? 7. How is yellow between red and blue? 8. Why is there no pink light? 9. What use is light we can t see? 10. How does a laser work? Or, is light really a wave?
Concave and convex lenses utilize refraction by shaping glass to focus light -> lens converging lens bi-convex has two convex surfaces diverging lens bi-concave has two concave surfaces
Variety of lenses utilize refraction by shaping glass to focus light -> lens
Ac'vity 12: PhET Lab
Different focal lengths create images at different loca'ons Short focal length = fat lens And smaller image Like a larger droplet Long focal length = thin lens This is related to the power of the lens. Which would you say is more powerful? And larger image Like a larger droplet
Two ways to tell where the image is: 1. Lens equa'on will tell you the distances 1 + 1 = 1 d O d I F 2. Principle rays will help you locate it graphically
Ray Tracing for lenses: Rule #1: Rays aimed at center pass straight through the lens Rule #2: Rays aimed parallel to axis con'nue through the focal point (on the other side) Rule #3: Rays aimed through focal point (on one side) con'nue out parallel (on the other side) Image 9
Case 1: Object distance x o Image distance x i So this makes a real, smaller, upside down image. Focal length F 10
Now you prac'ce! Use a ruler! If you finish, check your answers with lens equa'on Rule #1: Rays aimed at center pass straight through the lens Rule #2: Rays aimed parallel to axis con'nue through the focal point (on the other side) Rule #3: Rays aimed through focal point (on one side) con'nue out parallel (on the other side) Which one(s) is a magnifying glass? Which one(s) is like the water droplet? 11
So this is a virtual, larger image. i.e, magnifying glass. Rule #1: Rays aimed at center pass straight through the lens Rule #2: Rays aimed parallel to axis con'nue through the focal point (on the other side) Rule #3: Rays aimed through focal point (on one side) con'nue out parallel (on the other side)
Power of a lens: diopters Definition of diopter P in terms of f:!p (in diopters) = 1/f (in meters) - positive for convergent lenses (positive f), negative for diverging lenses (negative f) Meaning of P: - P is a measure of the ray bending power of the lens - eyeglasses and contact lens prescription is given in diopters, P
clicker question Diopters Q: What is the focal length of eyeglasses with prescription of -2.0 diopters? a) (a) 1 meter b) (b) - 1-1 meter c) 0.5 meter d) - 0.5 meter (c) 0.5 meters (d) -0.5 meters!p (in diopters) = 1/f (in meters) A: -2.0 diopters = 1/f -> f = 1/(-2.0 diopters) -> f = -0.5 meters
Combining lenses using diopters Diopters power of a multi-lens combination? P AB = P A + P B Example: - lens A, f A = 0.5 m - lens B, f B = -1 m - What is the power of combined lens? - What is the focal length f AB of combined lens? Solution: - power of lens A is 1/(0.5) = 2 diopters - power of lens B is 1/(-1) = -1 diopters - combined lens P AB = P A + P B = 2 + (-1) = 1 diopters - focal length of a combined lens, f AB = 1/P AB = 1 m - only valid for touching thin lenses
As you make the index of refracmon of the lens greater, what happens to the posimon of the image? A. The image remains where it is B. The image moves closer to the lens C. The image moves further from the lens. Answer is B: Higher n = more bending power PhET, guides U2L06 16
What is effect of increasing n? Remember, as you increased n of lens, light bent more So the greater the difference in n between the materials, the more light will bend as it goes through lens
Light bends more when the difference in n is greater. So consider: A converging lens is made of glass (n glass = 1.6). The glass is placed in air (n=1), rays converge at the focal point, as shown. When the lens is placed in water (n water = 1.33), will the rays converge: A) At the same point B) At a further distance from the lens C) At a closer distance to the lens Focus op'cal axis PhET f
n (glass) = 1.5 n (air) = 1.0 n (water) = 1.3
n (glass) = 1.5 n (air) = 1.0 n (water) = 1.3 So answer is B This is why you can t see clearly underwater! The lens of your eye isn t focusing the light where it usually would (the re'na)
Diverging, or concave lens Diverging Lens: f < 0
Lens equa'on: 1 d o + 1 d i = 1 f Diverging Lens: f < 0 An object is placed is placed near a diverging lens, but the object is further from the lens than the focal length of the lens. The image formed is virtual.
An object is placed is placed near a diverging lens, but the object is further from the lens than the focal length of the lens. The image formed is.. A) Real B) Virtual C) there is no image.
Diverging (concave) lenses 1 2 3 Rule #1: Rays aimed at center pass straight Rule #2: Rays aimed through the lens parallel to axis con'nue through the focal point (on the other side) Rule #3: Rays aimed through focal point (on opposite side) con'nue out parallel 24
Diverging (concave) lens What do you no'ce?
Which person is wearing a convex (converging) lens? A) The one on the lek B) one on right C) Both D)??? Convex: Object close to lens appears magnified Object far away looks small and upside down Reading glasses are convex! The concave lens makes things look small, no maler how close the object is! Farsighted glasses are concave!
Summary: Converging (convex) and Converging: diverging (concave) lenses Nearby object appears magnified (and virtual) Far away object is smaller (and real) Diverging Far away object looks closer (and smaller, and virtual)
Summary of the meaning of negative number in the lens and magnification equations Negative focal length, f, means the lens is diverging. Otherwise it is converging. Negative magnification, M, or negative image height, S o, means the image is upside down (inverted) relative to the object. Negative image distance, x I, means the image is on the same side of the lens as the object (a virtual image; rays don t really come from that place. Otherwise, image is real) 1/f = 1/x i + 1/x o M = -x i /x o