Physics 1230: Light and Color. Guest Lecture 18 Jack Houlton Lenses, Rays, and Math!

Transcription

1 Physics 230: Light and Color Chuck Rogers, Ryan Henley, Valyria McFarland, Peter Siegfried physicscourses.colorado.edu/phys230 Guest Lecture 8 Jack Houlton Lenses, Rays, and Math! Online and Written_HW0 due WED. 8PM EXAM 2 in class on Thursday this week!

2 Physics 230: Light and Color Chuck Rogers, Ryan Henley, Valyria McFarland, Peter Siegfried physicscourses.colorado.edu/phys230 Projects See the Projects tab on the website. Time to think about ideas and form groups. First list of possible project topics and group members, due Friday (0 points of 65 total). 2

3 Last Time: Thin convex (converging) lens } If the glass surface is nearly a section of a sphere, it will FOCUS parallel rays. focal length A THIN LENS is very thin compared to the focal length. Then we can simplify the treatment with THREE SIMPLE RULES. F F foci 3

4 Last Time: Converging lens Ray tracing rules ) A ray parallel to the axis is deflected through the focus on the other side 2) A ray through the center of the lens continues undeviated 3) A ray coming from the focus on one side goes out parallel to the axis on the other focal length foci} 2 3 F 3 F 4

5 Ray tracing: Thin lens, object outside focus Amazing property of this lens: all rays from the tip of the arrow will converge to the same point (the image) The Lens acts as our Magic Ray Machine, creating the rays to produce an image. Eye sees an image here. 5

6 Clicker question In this case, the image is: A) Virtual B) Real Eye sees an image here. 6

7 Clicker question In this case, the image is: A) Virtual B) Real Real because the light rays really go through the image. You can put a screen there to see it. Eye sees an image here. 7

8 Ray tracing exercise

9 Ray tracing a convex lens: object inside focus 9

10 Ray tracing a convex lens: object inside focus The image appears larger (and farther away) than the object. This is a magnifying glass. (Remember: a magnifying glass is a convex lens.) Aside: near-sighted people need concave/diverging lenses; can a marooned myopic start a fire with his eye-glasses? 0

11 Converging/convex lens: Near objects are magnified and upright. Far objects are upside down and smaller Near object (words) Far object (bridge!) Magnifying glass makes words appear larger Water drops act as convex focusing lenses. Images are smaller and inverted

12 Thin concave (diverging) lens Guess how this ray will be bent: F F 2

13 Thin concave (diverging) lens: Ray tracing rules ) A ray parallel to the axis is deflected as if it came from the focus 2) A ray through the center of the lens continues undeviated 3) A ray aimed at the focus on the other side comes out parallel 2 F F 3 Ray might have to be extended

14 Difference between concave and convex rules F F (Rule 3, the backwards version of rule, also differs) F F 4

15 Thin concave (diverging) lens image F F (A) Or (B): The image is LEFT or RIGHT of the lens. The image is REAL or VIRTUAL. The image appears smaller (and closer) than the object. 5

16 Clicker question mask 2 lens screen Two point sources of light are imaged onto a screen by a converging lens. The images are labeled and 2. You slide a mask over the left half of the lens. What happens to the images? A) Image vanishes B) Image 2 vanishes C) Something else happens The image gets dimmer, but it still produces a pair of images.

17 REMEMBER: There are rays going out to the entire lens. All of them help form the images. Even a small part of a lens is still a lens. It can form images.

18 Take a long breath Ray tracing lets you predict how lenses and images work. Guaranteed to Work! It is not the only way We have a mathematical way too.

19 Object distance, image distance, focal length X o X i F Notice all the triangles There are going to be connections between Xo, Xi, and F. 9

20 Magnification formula S 0 = object height S i = image height Note the similar triangles. Demo: big mama lens and bulb Image height below the horizontal axis? Then it is defined as negative. 20

21 Object distance, image distance, focal length X o X i F F SO SI X S O I Notice all the triangles There are going to be connections between Xo, Xi, and F. 2

22 Object distance, image distance, focal length X o X i F F SO SI X S O I OR SI SO X I X O F X X X X I I O I 22

23 The lens equation: The land of One-Over-Everything! F = focal length X O = object distance X I = image distance Usually, F and X O are given. We want to find X I X O X I X I F F X O Distant objects: Let X o be very large, say,000,000 meters. Then /X o = , which is very small. You can ignore it. Then For distant objects, X I F Demo: find focal length of lenses the image is at the focal point (ask a burnt ant) 23

24 The lens equation: The land of One-Over-Everything! F = focal length X O = object distance X I = image distance Usually, F and X O are given. We want to find X I When are the object distance to the lens and the image distance from the lens equal?? Demo: find focal length of lenses 2 X F I X O X I X I F F X O OR 2 X X F I O 24

25 Good place for questions!

26 The lens equation gives the same results as ray-tracing but without any rays! /x 0 + /x i = /f f is focal length of lens x o = positive distance from object to center of lens (when object is left of the lens) x i = distance from image to lens center x i is a positive number for (real) image on other side of lens from object. x i is a negative number for (virtual) image on same side as object. Given two, find the third. Can use the lens equation to find image position if know object position or vice versa, without any rays x o f f x i (will be positive number for this case)

27 Here is one example of how to use the lens eqn with a converging lens Given: f = 0 cm Object is 5 cm in front of lens: x 0 = 5 Find: Where is image and is it real or virtual? Solve equation for x i : Substitute numbers for letters Subtract /5 from both sides Arithmetic on calculator Multiply by x i /0.033 = + 0 f x5 o x i 0-5 = x i = x i x i = = 30 cm.033 Image is 30 cm to right of center of lens and is real because x i is positive

28 Here is a sketch to show the previous result We can verify our result by ray-tracing f = 0 x o = 5 x i = 30

29 Here is an example of how to use the lens eqn with a diverging lens Given: Find: f = 5 cm NOTE, THE FOCAL LENGTH OF A DIVERGING LENS IS NEGATIVE Object is 2 cm in front of lens: x 0 = 2 Where is image and is it real or virtual? Solve equation for x i : Substitute numbers for letters Subtract /2 from both sides Arithmetic on calculator Multiply by x i /(-0.283) = + -5 f x2 o x i - = -5 2 x i = x i x i = = cm Image is 3.53 cm to left of center of lens and is virtual because x i is negative

30 Summary of the meaning of negative number in the lens and magnification equations Negative focal length, f, means the lens is diverging. Otherwise it is converging. Negative image distance, x i, from image to lens means the image is on same side as object and virtual (rays coming from it never really meet) Otherwise image is real Negative image distance, x I, means the image is on the same side of the lens as the object (a virtual image). Negative magnification, M, means the image is upside down (inverted) relative to the object. /f = /x i + /x o M = -x i /x o

31 Questions: Always! (A) Or (B): The object distance is POSITIVE or NEGATIVE? The image distance is POSITIVE or NEGATIVE? The image height is POSITIVE or NEGATIVE? Both above or below? Same side means 3

32 The lens equation: The land of One-Over-Everything! F = focal length X O = object distance X O X I F X I = image distance Usually, F and X O are given. We want to find X I X I F X O Eventually you start to use /everything with ease. Then give those things a name! Demo: find focal length of lenses Call /F the LENS POWER. The units are DIOPTERS or /meters. 32

33 Lens Power (or diopters) Lens power: D = /F Units of D are /meters, also called diopters Eyeglass lenses are measured in diopters. Example: D = 2/m = what focal length? F = /D = /(2/m) = (/2) m = 0.5 m

34 Good place for a break! Enjoy your day. 34