1. Refraction and Lenses

2. Refraction is the bending of light as it moves from one medium to a medium with a different optical density. This bending occurs as a result of the speed of light changing at the interface between the two media.

3. Refraction Notice the spoon appears to bend where it enters the water.

5. The light ray that hits the interface is called the incident ray. The angle between the refracted ray and the normal is called the angle of refraction. The light ray that passes into the new medium is called the refracted ray. The angle between the incident ray and the normal is called the angle of incidence. At the point where the incident ray hits the interface, a normal (perpendicular) to the surface should be drawn.

6. Incident Ray Angle of Incidence Refracted Ray Angle of Refraction Normal Interface between 2 media

7. As light strikes the interface between two media with different optical densities at an oblique (not 90 o ) angle, it changes speed and is refracted. As it moves from a less dense medium to a more dense medium, it bends toward the normal (perpendicular to the interface) and slows down. Less More

8. As it moves from a more dense medium to a less dense medium, it bends away from the normal and speeds up. Less More

9. If the light strikes the interface at a 90 o angle, it is not refracted and continues moving in a straight line but its speed will change.

10. When light passes through a parallel sided glass figure, the emergent ray will be parallel to the incident ray because the amount it is bent toward the normal as it enters the glass is the same amount it bends away from the normal as it leaves the glass.

11. air glass Incident Ray Normal Refracted Ray Normal Emergent Ray

12. Light rays that strike the parallel sided glass figure perpendicular to the side will pass straight through the piece of glass without bending.

13. Light is also refracted by the same rules when it goes through an object that does not have parallel sides. However, in this case, the emergent ray will not be parallel to the incident ray. As the light ray enters the prism, it is moving from a less dense to a more dense substance so it is bent toward the normal. As the light ray leaves the prism, it is moving from a more dense to a less dense substance so it is bent away from the normal.

14. In the picture shown below, the light source is on the right side. Notice the bending as the light travels through the prism, when it leaves the prism the white light has been separated into its component colors. This separation is due to the fact that each different wave length of light moves at a slightly different speed in glass and is therefore refracted at slightly different amounts.

15. Index of Refraction The index of refraction of a substance is the ratio of the speed light will travel in a vacuum compared to the speed light will travel in the substance. n s = c / v s N s is the index of refraction of the substance c is the speed of light in a vacuum which is 3 * 10 8 m/s v s is the speed of light in the substance

16. Snell’s Law n 1 sin  1 = n 2 sin  2 22 n2n2 n1n1 11 Shows the mathematical relationship between the index of refraction and the amount that light is refracted as it enters the substance.

17. We are able to see most objects not because they are emitting light but because they reflect light. When you are looking into a pond, at many angles you are able to see the fish below the water but he is not exactly where you appear to see him. Image Object

18. When the light reflected from the fish hits the surface of the water at what is called the critical angle, the light is refracted along the surface of the water. The critical angle occurs when the angle of refraction is 90 o. It can be calculated using the equation  1 = sin -1 (n 2 / n 1 )

19. When light is reflected from a fish and it hits the surface of the water at an angle greater than the critical angle all of the light is reflected back into the water and none is allowed to escape. This is called internal reflection.

21. Fiber Optic Cables Light is transmitted along a fiber optic cable due to the phenomenon of total internal reflection.

23. Internal Reflection

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

25. Types of Lenses Convex lenses are also known as converging lenses since they bring light rays to a focus. Concave lenses are also known as diverging lenses since they spread out light rays.

26. 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

27. The distance from the lens to the focal point is called the focal length. Typically, a point is also noted that is 2 focal lengths from the lens and is labeled 2f. f2f f f f Principle axis Convex Lens Concave Lens The principle axis is a line which connects the focal point and the 2f point and intersects the lens perpendicular to its surface.

28. Rules for Locating Refracted Images 1. 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. Light rays that travel parallel to the principle axis, strike the lens, and are refracted through the focal point (f). 3. Light rays that travel through the focal point (f), strike the lens, and are refracted parallel to the principle axis.

29. All three of these light rays will intersect at the same point if they are drawn carefully. However, the image can be located by finding the intersection of any two of these light rays.

30. Real images are images that form where light rays actually cross. In the case of lenses, that means they form on the opposite side of the lens from the object since light can pass through a lens. Real images are always inverted (flipped upside down). Virtual images are images that form where light rays appear to have crossed. In the case of lenses, that means they form on the same side of the lens as the object. Virtual images are always upright.

31. Images formed by Convex lenses

32. Locating images in convex lenses

33. Convex Lenses with the Object located beyond 2f

34. 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 beyond 2f

35. 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

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

37. Convex Lenses with the Object located at 2f

38. 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

39. 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

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

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

42. 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

43. 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

44. 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

45. Convex Lenses with the Object located at f

46. 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

47. 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

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

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

50. 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

51. 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

52. 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.

53. 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

54. Images formed by concave lenses

55. Locating images in concave lenses

56. Concave Lenses with the Object located anywhere

57. 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

58. 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

59. 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

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

61. The distance from the lens to the retina is fixed by the size of the eyeball. For an object at a given distance from the eye, the image is in focus on the retina. Although the image on the retina is inverted, the brain interprets the impulses to give an erect mental image. If the object moved closer to the eye and nothing else changed the image would move behind the retina the image would therefore appear blurred. Similarly if the object moved away from the eye the image would move in front of the retina again appearing blurred. To keep an object in focus on the retina the eye lens can be made to change thickness. This is done by contracting or extending the eye muscles. We make our lenses thicker to focus on near objects and thinner to focus on far objects.

62. 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.

63. 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.

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

65. 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

66. 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