Light and Optics

1. Light and Optics Refraction and Lenses

2. Introduction • Refraction: is the bending of light when the light passes from one medium to another air glass

3. Imagine you’re on a skateboard heading from the sidewalk toward some grass at an angle. Your front axle is depicted before and after entering the grass. Your right contacts the grass first and slows, but your left wheel is still moving quickly on the sidewalk. This causes a turn toward the normal. If you skated from grass to sidewalk, the same path would be followed. In this case your right wheel would reach the sidewalk first and speed up, but your left wheel would still be moving more slowly. The result this time would be turning away from the normal. Skating from sidewalk to grass is like light traveling from air to a more Axle Analogy “optically dense” medium like glass or water. The slower light travels in the new medium, the more it bends toward the normal. Light traveling from water to air speeds up and bends away from the normal. As with a skateboard, light traveling along the normal will change speed but not direction. overhead view sidewalk grass r

4. Introduction Useful terms to describe refraction of light angle of incidence angle of reflection normal incident ray air glass refracted ray angle of refraction

5. air glass Introduction From a less dense to a denser medium Example: from air to glasslight is benttowards the normal. normal incident ray refracted ray

6. water air Introduction From a denser to a less dense medium Example: from water to air light is bentaway from the normal. normal incident ray refracted ray

7. Laws of refraction • The incident ray, the refracted ray , the reflected ray, and the normal all lie in the same plane, i.e., 2-Dimensional. normal normal incident ray air air glass glass refracted ray refracted ray

8. c v n = The index of refraction of a substance is the ratio of the speed in light in a vacuum to the speed of light in that substance: Index of Refraction, n Medium Vacuum Air (STP) Water Ethanol Glass Diamond n 1 1.0002 1.33 1.36 ~1.5 2.42 n = Index of Refraction c = Speed of light in vacuum v = Speed of light in medium Note that a large index of refraction corresponds to a relatively slow light speed in that medium.

9. i ni Snell’s Law nr r Snell’s law states that a ray of light bends in such a way that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. Mathematically, nisini = nr sinr Here ni is the index of refraction in the original medium and nr is the index in the medium the light enters. iandrare the angles of incidence and refraction, respectively. Willebrord Snell

10. Example Problem Light in air is incident upon a piece of crown glass (n=1.52) at an angle of incidence of 45º. What is the angle on refraction?

11. Convex/Converging Lenses

12. Concave/Diverging Lenses

13. Ray Tracing for Lenses Ray #1: Parallel to the axis Refracts through F Ray #2: Through F Refracts parallel to axis Ray #3: Through Center of lens undeflected • Light passes through a lens • There is a focal point on both sides of a lens Converging Lens:

14. Example: Camera

15. For a Diverging Lens: Now, for Diverging lenses…… Web Link: Spherical mirrors and lenses Ray #1: Parallel to the axis on the left Refracts as if it came from F on the left Ray #2: Heads toward F on the right Refracts parallel to the axis on the right Ray #3: Through the center of the lens undeflected

16. Example: Glasses to correct nearsightedness 2

17. But the variables are defined slightly differently now because………. For a lens, a real image is on the opposite side as the object For a mirror, a real image was on the same side as the object These equations also work on lenses: The Thin Lens Equation The Magnification Equation

18. Focal length (f) + converging - diverging Sign conventions for Lenses Object distance (do) + object on the left Image distance (di) + image on the right (real) - image on the left (virtual) Magnification (m) + upright - inverted