Physics 9 Wednesday, February 17, 2016

Transcription

1 Physics 9 Wednesday, February 7, 206 On Wednesday, I will be out of town. Zoey Davidson will be here, in my place, to work some mirror and lens examples with you, probably on worksheets: try ray-tracing; try f = d o + d i ; compare what you and your neighbor get with what Zoey does on the board; etc. Let s finish up where we left off on Monday with the convex lens, then work a bunch of example problems.

2 The trick for finding the image point graphically: draw the easy-to-draw rays ( principal rays ), and see where they meet. For thin converging lens, what comes in parallel to axis on LHS must pass through focus on RHS. What passes through focus on LHS must exit parallel to axis on RHS. What passes through the point at center of lens does not bend. (There are analogous tricks for mirrors, thin diverging lenses, but thin converging lens is most useful case to remember.)

3 An object is placed 7 m to the left of a converging lens having focal length f = 5 m. Where does the image form? Let s try the equations first this time. hi di = +, = f do di ho do di = do f ho f, hi = do f f do

4 An object is placed 7 m to the left of a converging lens having focal length f = 5 m. Where does the image form? Object and image distances: = + f do di Magnification: m= di hi = ho do Image distance di is (A) +7.5 m (B) 7.5 m (C) +35 m (D) 35 m (E) +5 m

5 An object is placed 7 m to the left of a converging lens having focal length f = 5 m. Where does the image form? Object and image distances: = + f do di Magnification: m= di hi = ho do Magnification m is: (A) +0.4 (B) 0.4 (C) +2.5 (D) 2.5 (E) +5.0

6 An object is placed 7 m to the left of a converging lens having f = 5 m. Where does the image form? Where are the principal rays? Start with one that is horizontal on the left side of the lens.

7 An object is placed 7 m to the left of a converging lens having f = 5 m. Where does the image form? Next principal ray: passing through left focus.

8 An object is placed 7 m to the left of a converging lens having f = 5 m. Where does the image form? Next principal ray: passing through center of (thin) lens.

9 An object is placed 7 m to the left of a converging lens having f = 5 m. Where does the image form? Math gave d i = +7.5 m, m = 2.5. The graph qualitatively agrees, but my thick colored pencils missed the mark slightly.

10 hi di = +, = f do di ho do di = do f hi f, = do f ho f do For what values of do is the image inverted/upright? Real/virtual?

11 You ll work through more examples with Zoey on Wednesday.

12 Worksheet. Next, we draw the object (in this case, the actual light bulb), as a vertical arrow. In this special case, we re trying d o = 2f. The arrow s tip is a height h o > 0 above its base. The goal is to figure out where (if anywhere) the mirror forms an image of the point x = d o, y = h o.

13 The goal is to figure out where (if anywhere) the mirror forms an image of the point x = d o, y = h o. Starting from the tip of the object, we draw the three easy-to-draw rays. I ve started one ray here: how do I continue it after it strikes the mirror?

14 The goal is to figure out where (if anywhere) the mirror forms an image of the point x = d o, y = h o. Starting from the tip of the object, we draw the three easy-to-draw rays. An incident horizontal ray is reflected through the focus.

15 The goal is to figure out where (if anywhere) the mirror forms an image of the point x = d o, y = h o. Starting from the tip of the object, we draw the three easy-to-draw rays. An incident horizontal ray is reflected through the focus. What happens to an incident ray that passes through the focus?

16 The goal is to figure out where (if anywhere) the mirror forms an image of the point x = d o, y = h o. Starting from the tip of the object, we draw the three easy-to-draw rays. An incident horizontal ray is reflected through the focus. An incident ray that passes through the focus is reflected as a horizontal ray. Two lines suffice to determine a point, but we ll do one more ray as a check.

17 The goal is to figure out where (if anywhere) the mirror forms an image of the point x = d o, y = h o. Starting from the tip of the object, we draw the three easy-to-draw rays. What happens to an incident ray that hits the mirror on the x axis, where the surface normal is horizontal?

18 The goal is to figure out where (if anywhere) the mirror forms an image of the point x = d o, y = h o. Starting from the tip of the object, we draw the three easy-to-draw rays. An incident ray that hits the mirror on the x axis is just mirrored across the x axis. (Alternative: a ray passing through the center of curvature comes right back on itself. That ray is harder to draw in this case.)

19 The goal is to figure out where (if anywhere) the mirror forms an image of the point x = d o, y = h o. In this case, the image is the same height as the object, but it is inverted. So h i = h o. We ll see from the math in a minute that if I had drawn more carefully, the rays would meet (in this example) at d o = d i. Imprecision is a limitation of the graphing method.

20 Worksheet 2. In this case, the object is at half the focal distance since f = R/2. Let s ray trace.

21 Worksheet 2. In this case, the object is at half the focal distance since f = R/2. For one ray, I need to start at the focal point to draw its trace through the arrow tip.

22 Worksheet 2. In this case, the object is at half the focal distance since f = R/2. This is the case where you hold the spoon close to your face. The image is virtual and magnified. From the math: f = + d o d i 4 = 2 + = d i = 4 d i

23 Worksheet 3....go to start of slides...

24 Worksheet 4. Same equations and ray tracing principles apply.

25 Worksheet 4. Same equations and ray tracing principles apply. But take care with the signs! f = + d o d i 6 = 2 + = d i = 4 d i

26 Worksheet 4. Same equations and ray tracing principles apply. But take care with the signs! f = + d o d i 6 = 2 + = d i = 4 d i m = d i d o What type of image?

27 Physics 9 Monday, February 5, 206 This week s reading: two more Giancoli chapters (24 & 25) about light and optics. Bill is back Friday!