1. Refraction and Lenses

2. The most common application of refraction in science and technology is lenses. The kind of lenses we typically think of are made of glass or plastic. The basic rules of refraction still apply but due to the curved surface of the lenses, they create images.

3. real image inverted image formed on the opposite side of lens as object formed where light rays actually converge (“cross”) visible on the screen (“projectable”) virtual image upright upright image image formed on the same side of a lens as object formed where light rays “appear” to cross not visible on a screen (not projectable)

4. REAL IMAGE FORMATION BY LENSES

5. VIRTUAL IMAGE FORMATION BY LENSES

6. The two main types of lenses are convex and concave lenses. The focal length (f) of a lens depends on its shape and its index of refraction.

7. A converging (convex) lens is thick in the center and thin at the edges. A diverging (concave) lens is thin in the center and thick at the edges.

8. Concave Lenses = Diverging Lenses spread out light rays. for nearsightedness (myopia) forms virtual images only always upright and reduced aka reducing lenses

9. Convex Lenses = Converging Lenses bring light rays to a focus. for farsightedness (hyperopia) form virtual images (upright & enlarged) aka magnifying Lenses Forms real images

11. CONVEX LENSES Where is the object when the image is the same size? Where is the object when there is no image?

12. The eye contains a convex lens. This lens focuses images on the back wall of the eye known as the retina.

13. VISION PROBLEMS:  MYOPIA is when image is formed in front of retina and is also known as nearsightedness and is corrected with a concave lens

14. VISION PROBLEMS:  HYPEROPIA is when image is formed behind the retina and is also known as farsightedness and is corrected with a convex lens

15. VISION PROBLEMS:  ASTIGMATISM is when the eye is shaped like a football rather than the normal eye that has a round shape similar to basketball. It causes certain amounts of distortion or pitched images because of the uneven bending of light rays entering the eye.

16. Parts of a Lens All lenses have a focal point (f). In a convex lens, parallel light rays all come together at a single point called the focal point. In a concave lens, parallel light rays are spread apart but if they are traced backwards, the refracted rays appear to have come from a single point called the focal point. f f Real Virtual

17. Lens Equation (1/f) = (1/d o ) + (1/d i ) f = focal length d o = object distance d i = image distance

18. Lens Magnification Equation M = -(d i / d o ) = (h i / h o ) M = magnification d i = image distance d o = object distance h i = image height h o = object height

19. Lens Sign Conventions f + for Convex lenses - for Concave Lenses d i + for images on the opposite side of the lens (real) - for images on the same side (virtual) d o + always h i + if upright image - if inverted image h o + always M + if virtual - if real image Magnitude of magnification <1 if smaller =1 if same size >1 if larger

20. Ex. 7 Camera lenses are described in terms of their focal length. A 50 mm lens has a focal length of 50 mm. Do cameras use converging or diverging lenses? What does d i represent? a. Where is the image (from the lens) of the above camera when it is focused on an object 3.0 meters away? b. What is the magnification of the image? c. If the object is 1.5 m tall, what is the height of the image? d. What is the di if the object is 6 m away? As the do increased, what happened to the di?

21. Rules for Locating Refracted Images 1. Start at top of object. Light rays that travel through the center of the lens (where the principle axis intersects the midline) are not refracted and continues along the same path. 2. Start at top of object. Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f).

22. Images formed by Convex lenses

23. Locating images in convex lenses

24. Convex Lenses with the Object located beyond 2f

25. f C f C Light rays that travel through the center of the lens are not refracted and continue along the same path. Convex Lens Object located beyond C

26. f 2f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f). Convex Lens Object located beyond 2f

27. f 2f f Image: Real Inverted Smaller Convex Lens Object located beyond 2f The image is located where the refracted light rays intersect

28. Convex Lenses with the Object located at 2f

29. f 2f f Light rays that travel through the center of the lens are not refracted and continue along the same path. Convex Lens Object located at 2f

30. f 2f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f). Convex Lens Object located at 2f

31. f 2f f Image: Real Inverted Same Size Convex Lens Object located at 2f The image is located where the refracted light rays intersect

32. Convex Lenses with the Object located between f and 2f

33. f2f f Light rays that travel through the center of the lens are not refracted and continue along the same path. Convex Lens Object located between f and 2f

34. f2f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f). Convex Lens Object located between f and 2f

35. f2f f Image: Real Inverted Larger Beyond 2f Convex Lens Object located between f and 2f The image is located where the refracted light rays intersect

36. Convex Lenses with the Object located at f

37. f2f f Light rays that travel through the center of the lens are not refracted and continue along the same path. Convex Lens Object located at f

38. f2f f Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f). Convex Lens Object located at f

39. f2f f No image is formed. All refracted light rays are parallel and do not cross Convex Lens Object located at f

40. Convex Lenses with the Object located between f and the lens

41. f 2ff Light rays that travel through the center of the lens are not refracted and continue along the same path. Convex Lens Object located between f and the lens

42. f 2ff Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f). Convex Lens Object located between f and the lens

43. f 2ff Convex Lens Object located between f and the lens These to refracted rays do not cross to the right of the lens so we have to project them back behind the lens.

44. f 2ff Image: Virtual Upright Larger Further away Convex Lens Object located between f and the lens The image is located at the point which the refracted rays APPEAR to have crossed behind the lens

45. Images formed by concave lenses

46. Locating images in concave lenses

47. Concave Lenses with the Object located anywhere

48. f 2ff Light rays that travel through the center of the lens are not refracted and continue along the same path. Concave Lens Object located anywhere

49. f 2ff Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f). Concave Lens Object located anywhere

50. f 2ff Image: Virtual Upright Smaller Between f and the lens Concave Lens Object located anywhere The image is located where the refracted light rays appear to have intersected

51. Someone who is nearsighted can see near objects more clearly than far objects. The retina is too far from the lens and the eye muscles are unable to make the lens thin enough to compensate for this. Diverging glass lenses are used to extend the effective focal length of the eye lens.

52. Someone who is farsighted can see far objects more clearly than near objects. The retina is now too close to the lens. The lens would have to be considerable thickened to make up for this. A converging glass lens is used to shorten the effective focal length of the eye lens. Today’s corrective lenses are carefully ground to help the individual eye but cruder lenses for many purposes were made for 300 years before the refractive behavior of light was fully understood.