2. 1© Manhattan Press (H.K.) Ltd. Terms used for lenses Images in lenses Images in lenses 12.2 Converging and diverging lenses Lens formula Lens formula Two thin lenses in contact Two thin lenses in contact Linear magnification Linear magnification

3. 2 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 207) Converging and diverging lenses Two types of lenses - converging (convex) lens (light rays converge to a point) - diverging (concave) lens (light rays diverge from a point)

4. 3 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 207) Converging and diverging lenses Converging lens Diverging lens

5. 4 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 207) Terms used for lenses Converging lens Diverging lens radii of curvature centres of curvature principal axis optical centre

6. 5 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 208) Terms used for lenses principle focus (F) focal length Converging lens

7. 6 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 208) Terms used for lenses Converging lens focal plane

8. 7 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 209) Terms used for lenses Diverging lens Focal length of diverging lens is -ve

9. 8 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 209) Terms used for lenses Power of a lens - ability to converge parallel rays Unit – dioptre (D) – 1 D = 1 radian per metre Go to More to Know 6 More to Know 6

10. 9 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 209) Images in lenses 1. Ray diagram - used to determine position and nature of image Ray 1

11. 10 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 210) Images in lenses Ray 2 Go to More to Know 7 More to Know 7

12. 11 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 210) Images in lenses Ray 3 Go to More to Know 8 More to Know 8

13. 12 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 211) Images in lenses 2. Image formed by a converging lens (a) Object at infinity at principal focus; inverted, diminished, real image

14. 13 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 211) Images in lenses 2. Image formed by a converging lens (b) Object distance u greater than 2f f < v < 2f; inverted, diminished, real image

15. 14 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 211) Images in lenses 2. Image formed by a converging lens (c) Object distance u = 2f v = u = 2f; inverted, same size, real image

16. 15 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 212) Images in lenses 2. Image formed by a converging lens (d) Object distance u between f and 2 f v > u; inverted, magnified, real image

17. 16 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 212) Images in lenses 2. Image formed by a converging lens (e) Object at principal focus (u = f) at infinity; upright, magnified, virtual image

18. 17 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 212) Images in lenses 2. Image formed by a converging lens (f) Object distance u less than f upright, magnified, virtual image (as magnifying glass)

19. 18 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 213) Images in lenses 3. Image formed by a diverging lens upright, diminished, virtual image

20. 19 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 213) Lens formula Lens formula - used to determine image distance lens formula

21. 20 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 214) Lens formula Note: 1. If the object is real, then the value of u is positive. If the image is real, then the value of v is positive. 2. If the object is virtual, then the value of u is negative. If the image is virtual, then the value of v is negative. 3. The focal length f of a converging lens is positive. The focal length f of a diverging lens is negative.

22. 21 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 214) Lens formula Real object - Rays diverging from point on object are incident on lens Virtual object - incident rays converge to point behind lens Go to Example 3 Example 3 Go to Example 4 Example 4

23. 22 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 215) Two thin lenses in contact Object (O) produces image (I’) by lens 1 I’ produces image (I) by lens 2 Go to Example 5 Example 5

24. 23 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 217) Linear magnification

25. 24 © Manhattan Press (H.K.) Ltd. 12.2 Converging and diverging lenses (SB p. 217) Linear magnification Go to Example 6 Example 6 Go to Example 7 Example 7

26. 25 © Manhattan Press (H.K.) Ltd. End

27. 26 © Manhattan Press (H.K.) Ltd. Power of a converging lens The larger the power of a converging lens, the nearer the emerging rays converged to the lens. Return to Text 12.2 Converging and diverging lenses (SB p. 209)

28. 27 © Manhattan Press (H.K.) Ltd. Spherical aberration The light rays near the edges of the lens and near the principal axis do not focus to the same point after refraction This phenomenon is called spherical aberration of lenses. Return to Text 12.2 Converging and diverging lenses (SB p. 210)

29. 28 © Manhattan Press (H.K.) Ltd. Chromatic aberration Since red light refracts less than violet light in glass (lens), a fringe of colours around the image is formed. The phenomenon is called chromatic aberration. Return to Text 12.2 Converging and diverging lenses (SB p. 210)

30. 29 © Manhattan Press (H.K.) Ltd. Q: Q: An object is at a distance of 20 cm from a converging lens of focal length 12 cm. Where is the image? Solution 12.2 Converging and diverging lenses (SB p. 214)

31. 30 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 12.2 Converging and diverging lenses (SB p. 214)

32. 31 © Manhattan Press (H.K.) Ltd. Q: Q: A converging beam of light incidents on a diverging lens of focal length 18.0 cm. If the beam is directed to a point 6.0 cm behind the lens, find the position of the image. Solution 12.2 Converging and diverging lenses (SB p. 215)

33. 32 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 12.2 Converging and diverging lenses (SB p. 215) f = –18.0 cm (the lens is a diverging lens) u = – 6.0 cm (the point O is a virtual object) Using the lens formula,

34. 33 © Manhattan Press (H.K.) Ltd. Q: Q: A thin converging lens of focal length 10 cm and a thin diverging lens of focal length 30 cm are placed in contact with each other. (a) Find the combined focal length. (b) Is the combination equivalent to a single converging or diverging lens? Solution 12.2 Converging and diverging lenses (SB p. 216)

35. 34 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 12.2 Converging and diverging lenses (SB p. 216) (b) The combined focal length is positive, thus the combination is equivalent to a converging lens.

36. 35 © Manhattan Press (H.K.) Ltd. Q: Q: An object is placed at a distance of 7.0 cm from a lens and a virtual image which is magnified eight times is produced. What are the focal length of the lens and the image distance? Solution 12.2 Converging and diverging lenses (SB p. 218)

37. 36 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 12.2 Converging and diverging lenses (SB p. 218)

38. 37 © Manhattan Press (H.K.) Ltd. Q: Q: A converging lens has a focal length of 20 cm. At what distance from the lens must an object be placed so that the linear magnification is of magnitude (a) 1, and (b) 4? Solution 12.2 Converging and diverging lenses (SB p. 218)

39. 38 © Manhattan Press (H.K.) Ltd. Solution: Return to Text 12.2 Converging and diverging lenses (SB p. 218)