Homework Notes

1. Homework Notes • If you are struggling with the homework, start working on it early enough that you can come to office hours if needed. • You can go to the help room even when one of us is not there, at least for the first half of the course. • Do not email me Wednesday night with homework questions.

2. Chapter 3: Mirrors and Lenses

3. Chapter 3: Mirrors and Lenses • Mirrors • Spherical mirrors • Ray tracing • Convex mirrors • Image formation • Applications • Concave mirrors • Image formation • Applications • Lenses • Refraction • Converging rays • Diverging rays

4. Reflection Review • Recall our ray tracing of a flat mirror • Recall that there are “special” rays that are sufficient for locating the image

5. Clicker Question • Which shows the correct location, orientation, and size for the image? A) B) C) D) E)

6. Spherical Mirrors

7. To find the normal to a curved surface at a point where a ray hits that surface (and will be reflected or refracted) First draw a tangent line to the curve (or tangent plane to the surface) The normal is perpendicular to that line or plane and going through the point Once you have drawn the normal you can draw the reflected or refracted ray What is the normal to a curved surface and how is it used to find rays?

8. Ray Tracing & Spherical Mirrors paraxial rays radius of curvature F C • Radius of Curvature: The radius of the sphere the mirror is “cut from” • Center of Curvature (C): The center of the sphere the mirror is cut from • Focal Point (F): The point where rays from a distance appear to converge • For a spherical mirror, the focal point is halfway between the surface and the center of curvature • Paraxial Ray: A ray coming on to the mirror parallel to the axis

9. Convex vs. Concave • Spherical mirrors are drawn in two dimensions, so you have to imagine the 3D mirror this line represents • Both convex and concave mirrors obey the same law of reflection, but they make different kinds of images Convex Concave

10. Sources of Paraxial Rays • The rays coming from a distance source can be considered approximately paraxial when they reach a mirror Convex mirror • The rays from a nearby source, such as a candle or bare light bulb, cannot be considered paraxial

11. Special Rays: Convex Mirror axis F C Ray 1 Rule: All rays incident parallel to the axis are reflected so that they appear to be coming from the focal point, F.

12. Special Rays: Convex Mirror axis F C Ray 2 Rule: All rays that (when extended) pass through C are reflected back on themselves

13. Special Rays: Convex Mirror axis F C Ray 3 Rule: All rays that (when extended) pass through F are reflected back parallel to the axis.

14. Locating an Image: Convex Mirror axis F C • Image properties: • virtual (behind the mirror) • right-side up • closer to the mirror than the object • smaller than the object.

15. Compare to Flat Mirror • Image properties: • virtual (behind the mirror) • upside down • the same distance from the mirror as the object • the same size as the object

16. Clicker Question • The image formed in a convex mirror is smaller than the object. This would make a convex mirror useful for which application? • Makeup or shaving mirror • Wide-angle mirror, such as on a car or a blind intersection • A mirror in a clothing store dressing room

17. Convex Mirrors • Because the image is smaller than the object, convex mirrors reflect from wider angles than flat mirrors.

18. Concave Mirrors C F axis Ray 1 Rule: All rays incident parallel to the axis are reflected so that they pass through the focal point, F.

19. Concave Mirrors C F axis Ray 2 Rule: All rays that pass through C are reflected back on themselves

20. Concave Mirrors C F axis Ray 3 Rule: All rays that pass through F are reflected back parallel to the axis.

21. Image Formation: Concave Mirrors Object location: Between the center of curvature and the focal point C F • Image properties: • real (in front of the mirror) • upside down • farther from the mirror than the object • larger than the object.

22. Concave Mirrors Object location: Between the surface and the focal point C F • Image properties: • virtual (behind the mirror) • right-side up • farther from the mirror than the object • larger than the object.

23. Concave Mirrors Object location: Past the center of curvature C F

24. Concave Mirrors: Clicker Question Object location: Past the center of curvature C F Is the image Real and magnified Real and reduced Virtual and magnified Virtual and reduced

25. Clicker Question • The inside of a spoon bowl is a concave surface with a radius of curvature of a couple of inches (depending on the spoon). If you hold it about a foot from your face, what will your face look like? • Normal size, upside down • Normal size, right side up • Smaller, upside down • Smaller, right side up

26. Concave Mirrors: Application Because rays coming in parallel, as from a very distant source, are all reflected to the focal point, a receiver placed there will pick up the waves received over the large area of the dish, instead of just the small area of the receiver itself.

27. Concave Mirrors: Application • What if we put a light source at the focal point of a concave mirror? • All the rays emitted by the light go through the focal point, and are therefore reflected parallel to the axis of the mirror.

28. Spherical Lenses What if we don’t want to have to look at a reflection to magnify or reduce an image? We can use refractive optics instead (lenses)

29. Convex Glass Surface axis F C A concave surface is called “converging” because parallel rays converge towards one another

30. Convex Glass Surface F C axis The surface is converging for both air to glass rays and glass to air rays

31. Concave Glass Surface C F axis A concave surface is called “diverging” because parallel rays diverge away from one another

32. Concave Glass Surface F C axis Again, the surface is diverging for both air to glass rays and glass to air rays