Ch. 26: Geometrical Optics

Transcription

1 Sec. 6-1: The Reflection of Light Wave Fronts and Rays Ch. 6: Geometrical Optics Wave front: a surface on which E is a maximum. Figure 5-3: Plane Wave *For this wave, the wave fronts are a series of planes. Rays: lines drawn in the direction of propagation. Figure 6- point source Law of reflection: angle of incidence = angle of reflection Figure 6-3 Plane wave *At great distances, point source looks like plane wave. Angle of incidence: angle that incident ray makes with normal. Angle of reflection: angle that reflected ray makes with normal. 1

2 Figure 6-8 Figure 6-9 Spherical mirrors: shaped like a section of a sphere. mirror Figure 6-10 kinds of spherical mirrors: convex, concave Convex spherical mirror Concave spherical mirror Figure 6-11 Convex mirror Paraxial rays parallel to principal axis extend back to single point called focal point. Paraxial: near the principal axis Focal length: f = R (convex mirror) Sign convention: Distances behind mirror negative. Distances in front of mirror positive.

3 Figure 6-1 Concave mirror Sec. 6-4: Ray Tracing and Mirror Equation 3 important rays called principal rays: Paraxial rays parallel to principal axis now reflect back through focal point on same side of mirror. Focal length: f = R (concave mirror) 1. Parallel ray ( P ray ): ray coming in parallel to principal axis. Reflects through focal point.. Focal ray ( F ray ): ray drawn through focal point. Reflects parallel to principal axis. 3. Center-of-curvature ray ( C ray ): ray drawn through center of curvature. Reflects back along line of incidence. These rays determine the size and orientation of the image! Figure 6-14 Figure 6-15 Convex mirror 3

4 observer Figure 6-16 Figure 6-17 light rays appear to diverge from here Virtual image: no light rays really emanating from the image (no light at the location of the image). Summary: Convex mirrors Figure 6-18 Concave mirror (object distance d o > f) Behind mirrror Right-side up Smaller than object Virtual observer Object distance d o > R observer Object distance d o < R Inverted Smaller than object In front of mirror (closer to mirror than object is) real Inverted larger than object In front of mirror (farther away than object is) real 4

5 Example 6-3 Concave mirror (object distance d o < f) Figure 6-19 Deriving the Mirror Equation observer Right-side up larger than object behind mirror virtual ho = do hi di Mirror Equation: = 1 do di f Magnification: h m i h o d m= i d o Sec. 6-5: Refraction of Light Saw in Ch. 5 that speed of light in vacuum is c = m/s When light travels through a different material, it slows down: v= c n n is called the index of refraction of the material n vacuum = 1 (exactly) n air = n water = 1.33 n 1.5 glass Table 6-, p. 864 Light also bends (changes direction), when entering different material. This bending called refraction. 5

6 Figure 6-4 Exercise 6-4 Snell s Law: n sinθ = n sinθ 1 1 normal Willebrord Snell (161) normal nair 1.00 nair 1.00 nwater = 1.33 nglass 1.5 nglass =1.5 angles θ1 &θ measured relative to normal. when going from low n to high n, bends toward normal when going from high n to low n, bends away from normal Sec. 6-6: Ray Tracing for Lenses midline Thin lens approximation: In limit as slab gets thinner and thinner, can say that all refraction takes place pretty much at center (midline). Converging and Diverging Lenses: A First Look Figure 6-9 Figure 6-31 Figure 6-30 Two Basic Categories of Lenses: converging: focuses parallel rays so that they converge to a point on other side. diverging: bends parallel rays outward so that they diverge on other side. Converging (convex) Diverging (concave) nglass =1.5 nglass =1.5 focal point focal point 6

7 As with mirrors, can determine size and orientation of image by considering three important rays called principal rays: 1. Parallel ray ( P ray ): ray drawn parallel to principal axis. Focal ray ( F ray ): ray drawn through focal point 3. Midpoint ray ( M ray ): ray drawn through midpoint Diverging Lenses A Closer Look Parallel ray ( P ray ): parallel to principal axis. Refracted ray extrapolates back through focal point. Focal-point Ray ( F ray ): ray directed toward focal point on other side of lens. Refracts parallel to principal axis. Midpoint Ray ( M ray ): ray from object through midpoint of lens. Goes through undeflected. Figure 6-33 Figure 6-34 P P observer To find image, find intersection of all three principal rays on same side of lens as object Right-side up Smaller than object closer to lens than object is Virtual (there s no light really emanating from point P ) 7

8 Converging Lenses A Closer Look Figure 6-3 Locating image for converging lens is a bit more complicated than for diverging lens. Depends on where the object is located. Parallel ray ( P ray ): parallel to principal axis. Refracts through focal point on other side of lens. Focal-point Ray ( F ray ): passes through focal point on left side of lens (before hitting lens). Refracts parallel to principal axis. Midpoint Ray ( M ray ): passes through midpoint of lens undeflected. Figure 6-35 Sec. 6-7: The Thin-lens Equation Figure 6-36 ho h = i f di f (1) object farther away than focal point Image: on other side of lens inverted real can be smaller than object or larger than it object closer than focal point Image: on same side of lens as object right-side up virtual larger than object ho h = i do di () 1 = f do di (Thin-lens eq.) 8

9 Magnification: h m i h o d m= i d o p. 874: Sign conventions. Don t worry about virtual objects in last line. Read: Sec 6-1 Sec 6- Sec 6-3 Sec 6-4 Sec 6-5 (skip Total Internal Reflection, Total Polarization ) Sec 6-6 Sec 6-7 Skip: Sec 6-8 HW #8 (Chapter 6): CQ: 7, 13, 8 Probs: 3, 5, 11, 13, 18, 19, 1,, 37, 46, 47, 57, 59 (also calculate the image location), 74, 90 Take-home Quiz (Due Mon., Nov. 9): Prob. #7, Ch. 5 (end of chapter) 9