1. Today 2/7  Diverging Lenses--Ray Diagrams and Math  HW Questions?  Start reading chapter 26.6-8 on Lenses  HW:“2/7 Diverging Lens” (three pages) Due Wednesday 2/12  Exam IThursday, Feb 13

2. Lenses -- Wave Picture A converging lens bends light toward the axis

3. Converging Lenses Focal point is the place on the axis where all rays arriving parallel to the axis are directed There is a second focal point on the input side where all rays directed away from it leave parallel to the axis “In through focus-out parallel”“In parallel-out through focus” focal length

4. Converging Lens-Ray Diagrams ff d 0 object distance image distance d i Now we have to “backtrack” the rays to see where they seem to come from! f = +4cm d 0 = +2cm d i = -4cm h 0 = +1cm h i = +2cm m = +2 (no units)

5. Equations Thin lens equation Magnification equation f focal length always + for converging lens (- for diverging) d 0 object distance + if on input side d i image distance + if output side (- if on input side) m magnification + if image is (- if image inverted) h height + if not inverted (- if inverted)

6. Lenses -- Wave Picture A converging lens bends light toward the axis A diverging lens bends light away from the axis

8. Lenses -- Wave Picture A converging lens bends light toward the axis Focal point is a place on the axis where all rays directed parallel to the axis arrive

9. Lenses A diverging lens bends light away from the axis Now the Focal point is a place on the axis where all rays directed parallel to the axis seem to come from

10. Lenses Now the Focal point is a place on the axis where all rays directed parallel to the axis seem to come from There is a second Focal point on the axis. Any ray directed toward it from the far side are directed parallel to the axis.

11. Diverging Lens-Ray Diagrams ff Bend the ray at the middle of the lens In parallel-out as if from left focus Also straight through the center of the lens For lenses (both types) d i is positive on the right. Here d i will be a negative number. f is negative for diverging lenses. didi In as if toward right focus-out parallel

12. Diverging Lens-Ray Diagrams and Math ff didi d 0 = +12 cm, f = -4 cm find d i, m, h i

13. Virtual and Real Images Real:Virtual: A screen placed at the image will produce an image. A screen placed at the image will not produce an image. All image forming rays actually pass through the image. At most only one image forming ray will pass through the image.