1. LENSES: The three light rays ….. straight through the “center” through the focal point, and then (refract) parallel to the principle axis parallel to the principle axis, and then (refract) through the focal point

2. convex lens, object located beyond 2f: ray 1a… object 2f ff 2f

3. convex lens, object located beyond 2f: ray 2a… object 2f ff 2f

4. convex lens, object located beyond 2f: 2f ff 2f object ray 2b…

5. convex lens, object located beyond 2f: 2f ff 2f object ray 3a…

6. convex lens, object located beyond 2f: 2f ff 2f object ray 3b…

7. convex lens, object located beyond 2f: ** image is ….. 2f ff 2f object image ….. smaller, inverted, real, located between f & 2f your eyeball (but wait - it’s upside down!!)

8. other similar lens diagrams … except diagram #4 (slide #11) turns out weird

9. 2f ff 2f object convex lens, object located at 2f: ** image is ….. image ….. same size, inverted, real, located at 2f

10. 2f ff 2f image ….. larger, inverted, real, located beyond 2f object convex lens, object between f & 2f: ** image is …..

11. object 2f ff 2f...not found! (2 rays are parallel & never intersect!!) **Thus, there is “no image”, an “undefined image”, or it is also said that the image is “at infinity -  ”  convex lens, object located at f: ** image is …..

12. now for the really weird ones...

13. 2f ff 2f rays diverge (will never meet at a point) so must be backtracked! convex lens, between f & mirror: ** image is ….. object

14. 2f ff 2f rays diverge (will never meet at a point) so must be backtracked! convex lens, between f & mirror: ** image is ….. object image ….. larger, erect, virtual (located on the same side of the lens)

15. concave lens, with a negative focal point: ** image is ….. 2f ff 2f object rays diverge so must be backtracked! (sometimes this is called a “diverging lens”)

16. concave lens, with a negative focal point: ** image is ….. 2f ff 2f image ….. smaller, erect, virtual (located on the same side of the lens) rays diverge so must be backtracked! (sometimes this is called a “diverging lens”) object

17. Cam you see, by imagining a normal at all of the interfaces, that these three rays all really do follow the Snell’s Law?? Can you do them on your own - without looking, as you’ll be asked to on the test?? (Careful, the last one is very tricky!!) Coming up next: optics equations...

18. Optics Equations:Optics Equations: 1/f = 1/d O + 1/d I AND m = h O /h I =  d O /d I HW: Assume f = 10 cm (note f is negative for concave lenses) & h O = 1 cm. Now prove all 6 lens diagrams!! (But wait! You don’t actually have to do this, because they’re all exactly the same!! We just interpret “real” as being on the other side of a lens - instead of the same side of the mirror.) Misc notes: (a) the sun has d O = infinity (b) a planar mirror has f = infinty (c) the 4th mirror/lens diagrams have d I = 1 / 0 = infinty