Lenses in Optics
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The document discusses the principles of image formation using lenses and how lenses are used in corrective lenses. It covers the basics of refraction, how converging and diverging lenses form images using ray tracing rules, and examples of how converging and diverging lenses can correct for nearsightedness and farsightedness by forming intermediate images at the appropriate focal points for the eye. Diagrams illustrate the ray tracing and image formation for different types of lenses. Exercises provide examples of using the ray tracing rules to locate images.
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Lenses in Optics
- 7. What do these devices have in common?
- 8. Image Formation on Lenses Ray Tracing
- 9. Today • Refraction (background) • Converging Rays – Applications – Characteristics – Image formation through ray tracing – Exercises
- 10. Refraction • Light also goes through some things • The presence of material slows light’s progress – interactions with electrical properties of atoms • The “light slowing factor” is called the index of refraction – glass has n = 1.52 (meaning that light travels about 1.5 times slower in glass than in vacuum) – water has n = 1.33 – air has n = 1.00028
- 11. glass; n2 = 1.5 air; n1 = 1.0 A B Refraction at a plane surface Light bends at interface between refractive indices Bends more the larger the difference in refractive index normal line
- 12. Convex Glass Surface C axis A convex surface is called “converging” because parallel rays converge towards one another AIR (fast) GLASS (slow) normal line fast to slow bends towards the normal
- 13. Convex Glass Surface Caxis The surface is converging for both air to glass rays and glass to air rays AIRGLASS normal line slow to fast bends away from the normal
- 14. Caxis A concave surface is called “diverging” because parallel rays diverge away from one another Concave Glass Surface AIR GLASS
- 15. C axis Again, the surface is diverging for both air to glass rays and glass to air rays Concave Glass Surface AIRGLASS
- 16. Lenses converging lens “bi-convex” -has two convex surfaces diverging lens “bi-concave” -has two concave surfaces
- 17. CONVERGING LENS
- 18. Converging Lens • The focal point of a curved mirror was the image point of a distant star – It is the same for a lens. – The focal point of a converging lens is where the incoming rays from a distant star all intersect. • A distant star is used to guarantee that the incoming rays are parallel Focal point Focal distance
- 19. F’F Lenses optic axis 2F 2F principal axis secondary focal point primary focal point
- 20. F Similarly to a spherical mirror, incoming parallel rays are deflected through the focal point
- 21. Thin Lenses • Just as the ray tracing for mirrors is approximate and only accurate for certain situations, the ray tracing for lenses is accurate only for what are called “thin lenses” F’F thickness of lens distance to focal point
- 22. How is the image formed by a converging lens?
- 23. Converging Lens: Ray Tracing Rules Rule 1: Similarly to a spherical mirror, incoming parallel rays are deflected through the focal point. FF
- 24. Converging Lens: Ray Tracing Rules Rule 2: Rays passing through the center of the lens are undeflected, they continue straight through without being bent. Several rays are shown here as examples. FF
- 25. Converging Lens: Ray Tracing Rules Rule 3: The reverse of Rule 1, rays passing through the focal point are deflected to exit parallel to the axis FF
- 26. Major Rays used in Ray Tracing
- 27. The incident light ray from the object that is parallel to the principal axis will be refracted passing through the principal focal point after passing through the optic axis. Parallel Ray
- 28. F F’2F 2F’ Parallel Ray
- 29. The incident light ray that passes through the secondary focal point will be refracted parallel to the principal axis. Focal Ray
- 30. F F’2F 2F’ Focal Ray
- 31. The incident light ray that seems to pass through the optical center will not be refracted. Optic Ray
- 32. F F’2F 2F’ Optic Ray
- 33. F F’2F 2F’ Image
- 34. Exercises
- 35. F F’2F 2F’ (1) Locate the image and (2) Describe its characteristics Focal length = 5 cm Object’s location = 10 cm Object’s height = 3 cm Lens’ height = 8 cm
- 36. F F’2F 2F’ (1) Locate the image and (2) Describe its characteristics Focal length = 5 cm Object’s location = 5 cm Object’s height = 1 cm Lens’ height = 8 cm
- 37. DIVERGING LENS
- 38. F’F In diverging lens, parallel rays are deflected such that when extended backwards, they appear to be coming from the focal point on the other side. DIVERGING LENS
- 39. How is the image formed by a diverging lens?
- 40. Diverging Lens: Ray Tracing F’F Parallel rays are deflected so they appear to be coming from the focal point in front of the lens.
- 41. Diverging Lens: Ray Tracing F’F Just like for converging lenses, rays that pass through the center of the lens continue undeflected (straight) through the lens.
- 42. Diverging Lens: Ray Tracing F’F Rays that, if extended, would pass through the focal point on the other side of the lens, are deflected to be parallel to the axis.
- 43. Major Rays used in Ray Tracing
- 44. The incident light ray from the object that is parallel to the principal axis will be refracted as if it came from the secondary focal point. Parallel Ray
- 45. F F’2F 2F’ Parallel Ray
- 46. The incident light ray that seems to pass through the principal focal point will be refracted parallel to the principal axis. Focal Ray
- 47. F F’2F 2F’ Focal Ray
- 48. The incident light ray that seems to pass through the optical center will not be refracted. Optic Ray
- 49. F F’2F 2F’ Optic Ray
- 50. F F’2F 2F’ Image
- 51. Diverging Lens: Image Formation F’F The image is virtual*, reduced, and right side up.
- 52. F F’2F 2F’ (1) Locate the image and (2) Describe its characteristics Focal length = 5 cm Object’s location = 10 cm Object’s height = 3 cm Lens’ height = 8 cm
- 53. F F’2F 2F’ (1) Locate the image and (2) Describe its characteristics Focal length = 5 cm Object’s location = 5 cm Object’s height = 1 cm Lens’ height = 8 cm
- 55. Corrective Lenses: Myopia To correct myopia (nearsightedness), a diverging lens creates an intermediate image of a distant star at your far point so that your eye can see it even though the star is beyond your far point.
- 56. Corrective Lenses: Myopia To correct myopia (nearsightedness), a diverging lens creates an intermediate image of a distant star at your far point so that your eye can see it even though the star is beyond your far point. far point image of distant object
- 57. Corrective Lenses: Hyperopia To correct farsightedness your contact lens creates an (intermediate) image of a book 25 cm away at your near point so that your farsighted eye can see it even though the book is closer than your near point 25 cmnear point
- 58. Corrective Lenses: Hyperopia To correct farsightedness your contact lens creates an (intermediate) image of a book 25 cm away at your near point so that your farsighted eye can see it even though the book is closer than your near point near point 25 cm focal point of corrective lens
Editor's Notes
- Note that a lens has a focal point on both sides of the lens, as compared to a mirror that only has one focal point
- A lens is considered “thin” if the thickness of the lens is much less than the distance from the lens to the focal point.