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Understanding Refraction and Lens Equation in Optics

Learn about refraction, lenses, focal length, and image formation using ray diagrams. Explore converging and diverging lenses, focal points, and thin lens equation.

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Understanding Refraction and Lens Equation in Optics

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  1. PH 103 Dr. Cecilia Vogel Lecture 15

  2. Review • Refraction • index of refraction, law of refraction • Lenses • focal length • images • thin lens equation • ray diagrams Outline

  3. Lenses • Two types • converging • center thicker • sometimes called convex or positive • diverging • edges thicker • sometimes called concave or negative

  4. Converging Lens • Light comes in perpendicular to lens. • What happens to it, if it passes through : • top of lens • bent downward • center • straight thru (q=0) • bottom • bent upward • CONVERGE f • Demo of converging lens

  5. Diverging Lens • Light comes in perpendicular to lens. • What happens to it, if it passes through : • top of lens • bent upward • center • straight thru (q=0) • bottom • bent downward • DIVERGE f (negative) • Demo of diverging lens

  6. Focal Point and Images • Is focal point the point where light is in focus? • Only if rays come in parallel (from very far) • Image point is point where light is in focus • Position of image point depends on • position of object • type of lens • focal length of lens • Thin lens equation

  7. Ray Diagrams Step-by-step for converging lens: 0. Determine an appropriate scale. 1. Place lens, and draw an axis thru center of lens and perpendicular to it. 2. Draw an object (arrow) the object distance from lens. Make base of arrow on axis. 3. Place F one focal length behind lens on axis. 4. One ray from tip of arrow goes parallel to the axis until it hits the lens, then it goes out through F. (“P-ray”)

  8. 5. Second ray from tip of object goes through center of lens, and goes straight through. (“M-ray”) 6. Image of the tip of the arrow is where both outgoing rays seem to come from. 7. Optional check: place F’ one focal length in front of lens. 8. Optional check: Third ray through F’ continues until it hits lens, then goes out parallel to axis. (“F-ray”)

  9. Ray Diagrams Step-by-step for diverging lens: 0. Determine an appropriate scale. 1. Place lens, and draw an axis thru center of lens and perpendicular to it. 2. Draw an object (arrow) the object distance from lens. Make base of arrow on axis. 3. Place F one focal length in front of lens. 4. One ray from tip of object goes parallel to the axis until it hits the lens, then goes out as if it had come from F (that is, the outgoing ray is inline with F, but not though it). (“P-ray”)

  10. 5. Second ray from tip of object goes through center of lens, and goes straight through. (“M-ray”) 6. Image of the tip of the arrow is where both outgoing rays seem to come from. 7. Optional check: place F’ one focal length behind lens. 8. Optional check: Third ray headed toward F’ continues til it hits lens, then goes out parallel to axis. (“F-ray”)

  11. Ray Diagrams • Examples on board • f = +25 cm, do = 75 cm • f = +25 cm, do = 10 cm • f = -30 cm, do = 15 cm • Java applet

  12. Ray Diagrams • Check examples on board by calculation • f = +25 cm, do = 75 cm • f = +25 cm, do = 10 cm • f = -30 cm, do = 15 cm

  13. Lens Equations and Sign Conventions • do • positive if in front of lens • (negative if behind) • di • positive if behind • negative if in front • f • positive if converging • negative if diverging

  14. Lens Equations and Sign Conventions • ho • positive if up • negative if down • hi • positive if up • negative if down • M • positive if same side up • negative inverted

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