1. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science The Geometric Optics of Image Formation Graphical Ray Tracing

2. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Using Refraction to Focus Light. Glass Lens in Air n 1 =1 n 2 =1.5 Parallel Rays Focal point of lens Focal length of lens, f Optical Axis

3. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Glass Lens in Air n 1 =1 n 2 =1.5 Parallel Rays different direction Image Plane Parallel rays come to focus at one point on the image plane. Focal length of lens, f Optical Axis

4. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science A Chief Ray is a ray heading toward or away from the center of the lens. Glass Lens in Air n 1 =1 n 2 =1.5 Focal length of lens, f Examples of Chief Rays Optical Axis

5. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Thin Lens Approximation: Chief Rays pass through the lens without deviation. Glass Lens in Air n 1 =1 n 2 =1.5 Focal length of lens, f Examples of Chief Rays Optical Axis

6. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science We identify two very important rays: (A) Collimated Rays: These are the rays that are parallel to the optical axis. These rays come to focus at the focal point. (B) Chief Rays: These are the rays that go through the center of the lens on the optical axis. These rays are un-deviated.

7. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Thin Lens Optical Axis f Object Light from the object passes through the lens. Follow the Ray Tracing Rule Ray (A) passes through the focal point. Ray Tracing Rule: Select ONLY two tracing rays, one of type (A), and one of type (B), each from the tip of the object. (A) (B) Ray (B) is not deviated.

8. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Thin Lens Optical Axis f Object Light from the object passes through the lens. Follow the Ray Tracing Rule The point of intersection is where the tip of the object comes to a clear focus. (A) (B) All other rays from this point must come to focus at the same point.

9. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science This is how a projector works. f f h' h M = h' h Light Source Object is a slide

10. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Optical Axis f Object Magnification: The ratio of the size of the image to the size of the object. h' h M = h' h Magnification < 1 in this example, so the image is smaller than the object.

11. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Traditional Ray Tracing Terms Focal lengths for a thin lens in air: f = f' f' Object (collimated ray) (chief ray) f h h' L L' Object distance and height (L, h) Image distance and height (L, h)

12. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science Object distance = L Image distance = L' Try some different object locations, L. We observe 6 special cases. f f h' h M = h' h

13. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f h' = 0 h M = = 0 h' h Case (I) Object distance L =  Image formed at the focal point, and magnification = 0

14. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f h' h M = h' h Case (II) L between  and 2f. As object moves to the right, the image size increases. Image is real and inverted. eye looks small & inverted

15. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f h' h M = h' h eye looks small & inverted

16. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f h' h M = h' h 2f Case (III) At L = 2f, h = h', and M = 1. eye looks same size & inverted

17. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f h' h M = h' h 2f Case (IV): L between 2f and f, (a) the image is still inverted, and (b) h' > h, and M > 1. eye looks larger & inverted h' still increases as the object moves toward the lens.

18. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f h' h M = h' h 2f For L between 2f and f, (a) the image is still inverted, and (b) h' > h, and M > 1. looks much larger & inverted eye h' still increases as the object moves toward the lens.

19. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f h M = h' h 2f Case(V): L = f. The rays are parallel. They cross at infinity, so h' =  = M. This is the point of maximum confusion! eye looks very confusing

20. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f The rays diverge!! We look through the lens, and it is a magnifying glass! M = > 1 h' h h eye Case (VI): L between f and the lens. The rays diverge and look AS IF they come from an image that (a) is erect and (b) enlarged, h'>h, m > 1. This is called a "virtual image".

21. Imaging Science FundamentalsChester F. Carlson Center for Imaging Science f f The rays diverge!! We look through the lens, and it is a magnifying glass! M = > 1 h' h h eye This is called a "virtual image". This is how a magnifying glass works!