2. Light will refract (change direction) upon entering a new substance. If the new substance is more optically dense, the light will bend toward the normal. If the new substance is less optically dense, the light will bend away from the normal.

3. Air Water Normal Ѳ iѲ i Ѳ rѲ r (More Optically Dense than Air) When a ray of light moves into a substance that is more optically dense, the ray will bend in a direction that causes a smaller angle with the normal. Light refracts anytime it enters a medium that is different than the one from which it came.

4. Light will refract differently upon entering different substances. A Dutch scientist, Willebrord Snell (1591-1626), discovered a relationship between the sine of the angle of incidence with the sine of the angle of refraction (which is summarized in the following equation. Index of Refraction “n” = sin Ѳ I / sin Ѳ r n = sin 45 o /sin32 o n = 1.33 n = sin 45 o /sin28 o n = 1.5 n = sin 45 o /sin17 o n = 2.42 Vacuum

5. A man sees a fish below the surface of the water in a pond and attempts to throw a spear directly at the fish. Will he succeed in catching the fish? No, the fish is in a different location than what it appears to be. This is due to the refraction of light. As it enters the air it bends away from the normal.

7. For a ray traveling from one medium into another medium, Snell’s law can be written: n i sin Ѳ i = n r sin Ѳ r 45 0 60 0 ? ? (1.0) (sin 45) = (1.33) (sin Ѳ r ) Ѳ r = 32.1 0 (1.0) (sin 60) = (1.52) (sin Ѳ r ) Ѳ r = 34.7 0

8. Air Water (More Optically Dense than Air) V vacuum = 3.0 x 10 8 m/s Air (More Optically Dense than Space) Space (vacuum) * The speed of light is dependent upon the medium through which it travels. n air = c/v air 1.0003 = 3.0 x 10 8 m/s v air V air = 2.999 x 10 8 m/s n water = c/v water 1.33 = 3.0 x 10 8 m/s v water V water = 2.26 x 10 8 m/s

9. A ray of light approaches an air/glass boundary at an angle of 30 0 with the normal. Determine path of the ray through the following layers. Include all angles. 30 0 1.0 (sin 30 0 ) = 1.61 (sin Ѳ r ) Ѳ r = 18.093 0 1.61 (sin 18.093 0 ) = 1.33 (sin Ѳ r ) Ѳ r = 22.083 0

10. As you saw while performing your lab, the ray of light exits the glass at the same angle that it entered. This is due to the fact that the light is being refracted on the way into the glass as well as being refracted on the way out of the glass. Each refraction is at an air/glass boundary, therefore the angles are the same.

11. Prisms are capable of separating white light into the characteristic colors (ROYGBIV). This is done through the process of refraction. Light is refracted as it enters the prism and as it leaves the prism.

12. Refraction and Lenses

13. Lenses – An application of refraction There are 2 basic types of lenses A converging lens (double convex) takes light rays and bring them to a point. A diverging lens (double concave) takes light rays and spreads them outward.

14. Converging (double convex) Lens Much like a mirror, lenses also take light rays from infinity and converge them to a specific point also called the FOCAL POINT, f. The difference, however, is that a lens does not have a center of curvature, C, but rather has a focal point on EACH side of the lens.

15. Applications of Converging Lenses Obviously, converging lenses play an important role in our lives as our eyes are these types of lenses. Often times we need additional corrective lenses to fix our vision. In figure A, we see an eye which converges what we see on the retina. In figure B, we see an eye which converges too LATE. The eye itself is often too short and results in the person being far sighted (converging lens fixes this). In figure C, we see an eye which converges too SOON. The eye itself is often too long and results in the person being near sighted (diverging lens fixes this). In the later 2 cases, a convex or concave lens is necessary to ensure the image is on the retina.

16. Applications of Converging Lenses A camera uses a lens to focus an image on photographic film.

17. Ray Diagrams (converging lens) The rules for ray diagrams are the SAME for lenses as they were for mirrors except you go THROUGH the lens after refraction and instead of going through, C (center of curvature) you go through the actual center of the lens. ff Rule #1: Draw a ray, starting from the top of the object, parallel to the principal axis, then through “f” after refraction. Rule #2: Draw a ray, starting from the top of the object, through “f”, then parallel to the principal axis, after refraction. Rule #3: Draw a ray through the center of the lens.

18. Ray Diagrams As before, you draw the image down to the intersection as shown. ff Since this image could be projected on to a screen it is a REAL IMAGE and real images ALWAYS are found on the OPPOSITE side of the lens from the object. Likewise, virtual images would appear on the SAME SIDE as the object. The characteristics in this case are still inverted and reduced.

19. Converging Lenses (case scenarios) Case 1: Object beyond 2f Case 2: Object at 2f Case 3: Object between f and 2f Case 4: Object at f Case 5: Object inside f

20. Ray Diagrams (diverging lens) 1) Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point (i.e., in a direction such that its extension will pass through the focal point). 2) Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis. 3) An incident ray that passes through the center of the lens will in affect continue in the same direction that it had when it entered the lens.

21. Diverging Lenses (case scenarios) located on the object' side of the lens a virtual image an upright image reduced in size (i.e., smaller than the object)

22. Lenses – The Mirror/Lens Equation To CALCULATE the image’s position and characteristics you use the same equations you used for mirrors. An object is placed 35 cm in front of a converging lens with focal length of 20 cm. Calculate the image’s position relative to the lens as well as the image’s characteristics. 46.7 cm-1.33x This image is REAL (since the object distance is positive) and on the OTHER side of the lens. The image is INVERTED and ENLARGED.

23. Comparing Mirrors and Lenses LENSES The sign conventions for the given quantities in the lens equation and magnification equations are as follows: f is + if the lens is a double convex lens (converging lens) f is - if the lens is a double concave lens (diverging lens) d i is + if the image is a real image and located on the opposite side of the lens. d i is - if the image is a virtual image and located on the object's side of the lens. h i is + if the image is an upright image (and therefore, also virtual) h i is - if the image an inverted image (and therefore, also real) MIRRORS: The sign conventions for the given quantities in the mirror equation and magnification equations are as follows: f is + if the mirror is a concave mirror f is - if the mirror is a convex mirror d i is + if the image is a real image and located on the object's side of the mirror. d i is - if the image is a virtual image and located behind the mirror. h i is + if the image is an upright image (and therefore, also virtual) h i is - if the image an inverted image (and therefore, also real)

25. Total internal reflection can occur in glass, as seen with this coiled glass tube. The light ray is never allowed to escape the glass tube because it strikes the glass/air boundary at an angle that is greater than the critical angle.

26. Fiber optics makes it possible to use light instead of electricity to transmit voices and data. A standard 3-inch bundle of fibers can carry 14,000 telephone conversations. Fiber optics can also be used to explore the inside of the human body.

27. A rainbow is a spectrum formed when sunlight is dispersed by water in the atmosphere. Both refraction and total internal reflection are involved in the rainbow formation.

28. The pencil appears to split due to the refraction of light. Light from the pencil enters your eye after having traveled from a more dense medium into a less dense medium. This causes the light to bend away from the normal. This bending of the light gives the illusion of the pencil being somewhere that it actually is NOT.

29. * Diffraction is the bending of waves around the edges of barriers. Diffraction can cause wave interference as seen below. When light waves interfere constructively they cause areas of brighter light.

30. * Light that is allowed to pass through two slits will cause two different wave fronts that will interfere both constructively and destructively. The result is a pattern of bright and dark lines illuminating a screen paced behind the slits.

32. Central Bright Line 1 st Order Bright Line λ = xd/L L d x

33. A diffraction grating is simply a transparent material with very fine lines scratched into its surface. The clear spaces between the lines serve as slits through which light can be diffracted. Many beetles and butterflies produce their colors by means of diffraction. The butterfly’s wings are covered with tiny ridges only a few hundred nanometers apart. They each diffract the light hitting them, producing interference effects.