1. Unit 11: Part 2 Mirrors and Lenses

2. Outline Plane Mirrors Spherical Mirrors Lenses The Lens Maker’s Equation Lens Aberrations

3. Plane Mirrors The image formed by a plane mirror is upright, identical in size to the object, and as far behind the mirror as the object is in front of it.

4. Plane Mirrors The magnification is given by: For a plane mirror, M = +1.

5. Spherical Mirrors A spherical mirror is a section of a sphere. It may be concave or convex.

6. Spherical Mirrors A concave mirror (left) focuses incoming parallel rays at the focal point. A convex mirror bends incoming parallel rays outward, as though they came from a focal point behind the mirror.

7. Spherical Mirrors Images formed by spherical mirrors may be found by using the parallel, chief, and focal rays.

8. Spherical Mirrors For a concave mirror, the type of image formed depends on the position of the object.

9. Spherical Mirrors If the object is at the focal point, there is no image.

10. Spherical Mirrors The spherical-mirror equation is valid for any object position: Sign conventions for spherical mirrors are given on the next slide.

11. Spherical Mirrors

12. The magnification is given by:

13. Spherical Mirrors For a convex mirror the process is similar, but the image will always be virtual.

14. Spherical Mirrors Spherical aberration occurs because rays far from the mirror axis do not go through the focal point.

15. Lenses Spherical lenses have surfaces defined by two spheres.

16. Lenses A converging lens brings incoming rays together at the focal point.

17. Lenses The rays emerging from a diverging lens appear to have come from a single focal point.

18. Lenses Both converging and diverging lenses come in a variety of shapes.

19. Lenses Images formed by lenses can be found just as mirror images were found. The first two rays:

20. Lenses Locating and confirming the image:

21. Lenses The type of image formed by a converging lens depends on the position of the object. For a distant object:

22. Lenses For an object closer than the focal point:

23. Lenses

24. The thin-lens equation: Magnification:

25. Lenses A diverging lens always forms a virtual image.

26. Lenses In a multi-lens system, the image formed by the first lens becomes the object for the next.

27. The Lens Maker’s Equation We start with sign conventions:

28. 23.4 The Lens Maker’s Equation In general, each lens has two radii of curvature.

29. 23.4 The Lens Maker’s Equation This is the lens maker’s equation for a thin lens in air: The power of a lens may be described using diopters:

30. Lens Aberrations Spherical aberration occurs when rays far from the axis do not focus at the focal point.

31. Lens Aberrations Chromatic aberration occurs because the index of refraction depends slightly on wavelength, so light of different wavelengths focuses at different points.

32. Review Plane mirrors form virtual, upright, and unmagnified images. The object distance is equal to the image distance. The lateral magnification factor for all mirrors and lenses is: Focal length of a spherical mirror:

33. Review Spherical-mirror equation: Thin-lens equation:

34. Review Lens maker’s equation: Lens power in diopters: