Geometric Optics: Reflection, Refraction, and Image Formation

1. Chapter 34 Geometric Optics

2. Goals for Chapter 34 • To study reflection or refraction at a plane surface • To observe and calculate lateral magnification • To observe the focal length and focal point • To relate object and image distances • To consider thin lenses • To stipulate the sign rules on the optical axis • To see how optical elements are combined in cameras • To study the eye and ponder it as an optical instrument • To combine optical elements to make a simple magnifier • To consider microscopes and telescopes

3. Introduction • Lenses can correct vision problems. For someone wearing glasses or contacts, light entering the eye through the glasses or contacts is forced to focus on the retina instead of in front of it. • The surgeon in our photo is using combinations of optical elements to magnify a small surgical site.

4. Objects, images, and light rays • Light rays from a source will radiate in all directions, reflect from mirrored surfaces, and bend if the pass from a material of one index to another. • Consider Figures 34.1, 34.2, and 34.3.

5. Constructing the image from a plane mirror I • Following the light rays to form an image of an object. • Consider Figure 34.4. • Consider Figure 34.5.

6. Constructing the image from a plane mirror II • Consider Figure 34.6, below left. • Consider Figure 34.7, below right. Images from a plane mirror show left/right reversal.

7. Constructing the image from plane mirror(s) • Consider Figure 34.8, below left. Which image is reversed? • Consider Figure 34.9, below right. Multiple mirrors can create a host of virtual image possibilities.

8. Reflections from a spherical mirror • Images from a concave mirror change depending on the object position. Consider Figure 34.10. • Concave and convex mirror sign convention. Consider Figure 34.11.

9. The Hubble Space Telescope • The HST has a spherical mirror. Unfortunately, it was ground to the wrong dimensions by 1/50 the width of a human hair over a mirror as large as a person. • Replacing the mirror was unthinkable. The final solution was an electronic adjustment to the photodiode array which converts the optical image to digital data. • Consider Figure 34.12 at right to see the dramatic “before” and “after” images.

10. The focal point and focal length of a spherical mirror • The focal point is at half of the mirror’s radius of curvature. • All incoming rays will converge at the focal point. • Consider Figure 34.13.

11. A system of rays may be constructed to reveal the image • Rays are drawn with regard to the object, the optical axis, the focal point, and the center of curvature to locate the image. • Consider Figure 34.14 to view one such construct.

12. Images formed from concave mirrors • Follow Example 34.1. • Figure 34.15 illustrates Example 34.1. • Consider Conceptual Example 34.2.

13. The convex spherical mirror I • If you imagine standing inside a shiny metal ball to visualize the concave spherical mirror, imagine standing on the outside to visualize the concave spherical mirror. • Consider Figure 34.16 to introduce the convex spherical mirror.

14. The convex spherical mirror II • The convex spherical mirror cannot produce a real image regardless of the position of the object. Consider Figure 34.17 at top right. • Consider Santa’s problem in Example 34.3, illustrated by Figure 34.18 at bottom right.

15. A graphical method for mirrors • On slide 11, we hinted at a graphical formalism using the object, the center of curvature, the focal point, and the mirror plane. • Consider Figure 34.19 to view the entire formalism.

16. The graphical method for mirrors II • Read Problem-Solving Strategy 34.1. • Consider Example 34.4, illustrated by Figure 34.20 (shown below).

17. Refraction within a sphere • Perhaps as light traveling througha raindrop. • Consider Figure 34.21 and Figure 34.22.

18. Images formed by refraction • Consider Example 34.7, illustrated by Figure 34.26 at bottom left. • Consider Figure 34.27 (which is a “classic demonstration”).

19. Thin lenses I • The converging lens is shown in Figure 34.28. Note symmetrical focal points on either side of the lens. • Figure 34.29 uses the same ray formalism as we used with mirrors to find the image.

20. Thin lenses II • Figure 34.31 at bottom left illustrates a diverging lens scattering light rays and the position of its second (virtual) focal point. • Figure 34.32 illustrates some assorted common arrangements of lens surfaces. • Follow Example 34.8.

21. Graphical methods for lenses • Figure 34.36 applies to lenses the same ray-tracing method we used for mirrors.

22. The camera • A clever arrangement of optics with a method to record the inverted image on its focal plane (sometimes film, sometimes an electronicarray, it depends on your camera).

23. The eye—vision problems • When the lens of the eye allows incoming light to focus in front of or behind the plane of the retina, a person’s vision will not be sharp. • Figure 34.45 (at right) shows normal, myopic, and hyperopic eyesight.

24. Vision correction—examples • Follow Example 34.13, illustrated in Figure 34.49 in the middle of the page. • Follow Example 34.14, illustrated in Figure 34.50 at the bottom of the page.

25. The microscope • Optical elements are arranged to magnify tiny images for visual inspection. Figure 34.52 presents the elements of an optical microscope.

26. The astronomical telescope • Optical elements are arranged to magnify distant objects for visual inspection. Figure 34.53 presents the elements of an astronomical telescope.

27. The reflecting telescope • Optical elements are arranged to reflect collected light back to an eyepiece or detector. This design eliminates aberrations more likely when using lenses. It also allows for greater magnification. The reflective telescope is shown in Figure 34.54.