Exploring Refraction and Thin Lenses

1. Preview Section 1 Refraction Section 2 Thin Lenses Section 3 Optical Phenomena

2. What do you think? • Suppose you are reaching for swim goggles floating below the surface of a pool or trying to net a fish while out in a lake. Would you reach at the point where you see the object, or above it, or below it? • Describe personal experiences that helped you answer this question. • Make a sketch showing how you think light behaves when leaving the goggles, passing into the air, and then entering your eyes.

3. Refraction • Why does the lawnmower turn when it strikes the grass? • The right wheel slows down before the left one. • Light waves behave in the same way. • Refraction is the bending (change in direction) of light when it travels from one medium into another. • Caused by a change in speed

4. How does it bend? • Wave fronts (dashed lines) slow down when entering glass. • The lower edge slows before the upper edge, so the wave turns to the right. • Also, the wavelength is shortened. Upper edge Lower edge

5. Wave Model of Refraction Click below to watch the Visual Concept. Visual Concept

6. Ray Diagrams • Light rays reflect and refract. • If the light slows down, it bends toward the normal line (glass < air). • Angles are measured with the normal line. • Light rays are reversible.

7. Law of Refraction • c = 3  108 m/s • v is always less than c, so n >1 for all media. • nair = 1.000293 • n is dimensionless. • n is a measure of the optical density of a material.

8. Indices of Refraction

9. Snell’s Law • Angles must be measured with the normal.

10. Classroom Practice Problems • Find the angle of refraction of a light ray (589 nm) entering diamond from water at an angle of 30.00° with the normal. • Answer: 15.99° • A light ray (589 nm) traveling through air strikes an unknown substance at 60.00° and forms an angle of 41.42° with the normal inside. What material is it? • Answer: n = 1.309, so the material is ice

11. Refraction • Where does the cat see the fish? • Where does the fish see the cat? • Objects appear to be in line with the observed rays.

12. Now what do you think? • Suppose you are reaching for swim goggles floating below the surface of a pool. Would you reach at the point where you see the object, or above it, or below it? • Make a sketch showing how light behaves. • If you are under water looking at a person standing on the side of the pool, where is the image? • Make a sketch showing how light behaves.

13. What do you think? • How will the light bend as it enters and leaves the three glass blocks? • Draw the rays as they change direction. Make sure your drawing includes normal lines at each interface. • Would you describe the combination of blocks as converging or diverging with respect to the incoming light?

14. Lenses • A lens is a transparent object that converges or diverges light by refraction. • A converging lens is thicker at the middle. • A diverging lens is thinner at the middle. • Light actually bends at each surface. However, for thin lenses, we can show light bending only once at the center of the lens. • Focal length (f) is the distance from the focal point (F) to the center of the lens.

15. Converging and Diverging Lenses Click below to watch the Visual Concept. Visual Concept

16. Ray Diagrams for Lenses • Complete the ray drawing to locate the image using the rules above.

17. Ray Tracing for a Converging Lens Click below to watch the Visual Concept. Visual Concept

18. Images Created by Converging Lenses • Configurations 1 and 2:

19. Images Created by Converging Lenses • Configurations 3 and 4:

20. Images Created by Converging Lenses • Configurations 5 and 6:

21. Diverging Lens Diagram • Complete the ray diagram for the lens shown to the left using the three rules from Table 2.

22. Ray Tracing for a Diverging Lens Click below to watch the Visual Concept. Visual Concept

23. Thin-Lens Equations

24. Sign Conventions • p is positive if the object is in front of the lens. • q is positive if the image is behind the lens (real and inverted). • q is negative if the image is in front of the lens (virtual and upright). • f is positive for converging lenses and negative for diverging lenses. • h and h’ are positive if upright and negative if inverted.

25. Classroom Practice Problems • When an object is placed 3.00 cm in front of a converging lens, a real image is formed 6.00 cm in back of the lens. Find the focal distance of the lens. • Answer: 2.00 cm • Where would you place an object in order to produce a virtual image 15.0 cm in front of a converging lens with a focal length of 10.0 cm? How about a diverging lens with the same focal length? • Answers: 6.00 cm, -30.0 cm

26. The Eye and Corrective Lenses • Light is refracted at both the cornea (outer surface) and the lens. • When functioning properly, the converging lens can adjust so that the image is focused on the retina. • Muscles adjust the thickness of the lens. • Many people are nearsighted (myopia) and can’t see distant objects clearly. • Older people are often farsighted (hyperopia) and can’t see nearby objects. • The lens becomes inflexible with age and can’t be made thicker to focus on nearby objects.

27. Nearsightedness • The image forms in front of the retina, possibly because the retina is too long. • What type of lens is needed in front of the eye to correct the problem, converging or diverging? Explain your reasoning. • Answer: a diverging lens

28. Farsightedness • The image forms behind the retina, possibly because the lens is inflexible. • What type of lens is needed in front of the eye to correct the problem, converging or diverging? Explain your reasoning. • Answer: a converging lens

29. Combinations of Lenses • Microscopes and refracting telescopes use two lenses. • The objective lens forms a real image that is located inside the focal point of the eyepiece. • The eyepiece magnifies the first image, creating a large virtual image.

30. Compound Light Microscope Click below to watch the Visual Concept. Visual Concept

31. Refracting Telescope Click below to watch the Visual Concept. Visual Concept

32. Now what do you think? • How will the light bend as it enters and leaves the three glass blocks? • Draw the rays. • How is this similar to a lens? • Which type of lens? • How would the rays exit the three blocks if there were six equally spaced rays instead of three? • How would those same six rays exit a converging lens?

33. What do you think? • Suppose a beam of light entering a tank of water strikes at a 60.00° angle with the normal. What angle does it make with the normal after entering the water? Sketch it. • Suppose a beam of light emerging from beneath the water surface strikes at a 60.00° angle with the normal. What angle does it make with the normal after entering the air? Sketch it.

34. Total Internal Reflection • Total internal reflection occurs if the angle in the denser medium is too great. • Light can’t emerge so it is reflected back internally. • Occurs if the angle is greater than the critical angle (c). • Used in fiber optics, right angle prisms, and diamond cutting.

35. Critical Angle • c occurs when the angle in the less dense medium is 90°. • At the critical angle, the emerging ray travels along the surface. • At greater angles, the rays are totally internally reflected.

36. Total Internal Reflection Click below to watch the Visual Concept.

37. Classroom Practice Problems • Find the critical angle for light emerging from a diamond into air. The index of refraction for diamond is 2.419. Repeat for cubic zirconium with n = 2.200. • Answers: 24.42° for diamond and 27.04° for cubic zirconium • Which material is more likely to trap light entering the top surface in such a way that it reflects many times internally before emerging?

38. Atmospheric Refraction • Make a sketch like that above. On your drawing, show how light will bend when it strikes the atmosphere. • Remember that this is a very slight change in the index of refraction, and it occurs gradually as the atmosphere becomes denser. • This bending allows us to see the sun before it rises and after it sets.

39. Mirages • Mirages are caused by the refraction of light as it strikes the hot air near the earth’s surface. • This phenomena can be observed when driving on blacktop roads on hot summer days. • Inverted cars can be seen approaching, with the actual cars up above them.

40. Dispersion • Refraction or n depends on the wavelength. • Longer wavelengths refract less. • Prisms disperse the light into a spectrum. • Chromatic aberration is a lens problem where different colors focus at different points. • Can lead to imperfect images for cameras with less expensive lenses.

41. Rainbows

42. Dispersion of Light Click below to watch the Visual Concept. Visual Concept

43. Now what do you think? • How do fiber optic cables keep the light trapped inside the cable as it travels great distances and bends around corners? • What phenomena is responsible for trapping the light? • Why do different people see different colors for a water drop when observing a rainbow? • What phenomena is responsible for the rainbow?