Chapter 23:Mirrors and Lenses

1. Chapter 23:Mirrors and Lenses Homework assignment : 20,24,42,45,51 • Image of a point source The reflected rays entering eyes look as though they had come from image P’. P virtual image Flat Mirrors P’ Light rays radiate from a point object at P in all directions.

2. Image of a point source on a flat mirror (cont’d)

3. Flat Mirrors • Image formation on a flat mirror s’ (s) is the image (object) distance: |s| =|s’| • Sign Rules: • Sign rule for the object distance: • When object is on the same side of the reflecting • or refracting surface as the incoming light, the object • distance s is positive. Otherwise it is negative. • (2) Sign rule for the image distance: • When image is on the same side of the reflecting or • refracting surface as the outgoing light, the image • distance s’ is positive. Otherwise it is negative. • (3) Sign rule for the radius of curvature of a spherical • surface: • When the center of curvature C is on the same side • as the outgoing light, the radius of the curvature is • positive. Otherwise it is negative. s’

4. Flat Mirrors • Image of an extended object on a flat mirror image is erect image is virtual Multiple image due to multiple Reflection by two mirrors h h’ S’1 S’2 S’3 m = h’/h=1 lateral magnification

5. Flat Mirrors • Rotation of mirror When a flat mirror is rotated, how Much is the image rotated?

6. Flat Mirrors • Example What is the size of the smallest vertical plane mirror in which a woman of height h can see her full-length? Solution x x/2 The minimum length of mirror for a woman to see her full height h Is h/2 as shown in the figure right. (h-x)/2 h-x

7. Concave and convex mirrors Image Formed by Spherical Mirrors

8. Focal points at concave and convex mirror Image Formed by Spherical Mirrors Focal point or focus: Point F at which rays from a source point are brought together (focused) to form an image. Focal length: Distance f from mirror where focus occurs. f=R/2 where R is the radius of a spherical mirror.

9. Focal points at a concave mirror h object Image Formed by Spherical Mirrors d image s’ If

10. Image of an extended object at a concave mirror real image Image Formed by Spherical Mirrors Principle rays: Light rays that can be traced (more easily) from the source to the image: 1. Parallel to optical axis 2. Passing through the focal point 3. Passing through the center of curvature 4. Passing through the center of the mirror surface or lens

11. Magnification of image at a concave mirror h h’ Image Formed by Spherical Mirrors When s,s’ >0 , m<0 inverted s/s’<0, m>0 upright or erect

12. Example with a concave mirror Image Formed by Spherical Mirrors real image real image real image virtual image

13. Example with a concave mirror Image Formed by Spherical Mirrors

14. Image Formed by Spherical Mirrors • Image at a convex mirror s s’ f f R s positive s’ negative (virtual image) R negative f negative

15. Image Formed by Spherical Mirrors • Magnification of image at a convex mirror For a convex mirror f < 0 s’ m > 1 magnified m < 1 minimized m > 0 image upright m < 0 image inverted

16. Refraction at a convex spherical surface q1 q1-q2 Refraction at a spherical surface For small angles

17. Refraction at a concave spherical surface Refraction at a spherical surface For a concave surface, we can use the same formula But in this case R < 0 and f < 0. Therefore the image is virtual.

18. Relation between source and image distance at a convex spherical surface Refraction at a spherical surface s’ Snell’s law For a convex (concave) surface, R >(<) 0.

19. Example of a convex surface Refraction at a spherical surface

20. Example of a concave surface Refraction at a spherical surface

21. Example of a concave surface Refraction at a spherical surface

22. Example of a concave surface Refraction at a spherical surface

23. Sign rules for convex and concave lens: • Sign Rules: • Sign rule for the object distance: • When object is on the same side of the reflecting • or refracting surface as the incoming light, the object • distance s is positive. Otherwise it is negative. • (2) Sign rule for the image distance: • When image is on the same side of the reflecting or • refracting surface as the outgoing light, the image • distance i is positive (real image). Otherwise it is negative • (virtual image). • (3) Sign rule for the radius of curvature of a spherical • surface: • When the center of curvature C is on the same side • as the outgoing light, the radius of the curvature is • positive. Otherwise it is negative. Convex Lens

24. Lens-makers (thin lens) formula surface 2 surface 1 s’ Convex Lens Image due to surface 1: s’1 becomes source s2 for surface 2: R1>0 R2<0 s1 = s and s’2 = s’: Parallel rays (s=inf.) w.r.t. the axis converge at the focal pioint

25. Magnification s’ Convex Lens same as for mirrors

26. Object between the focal point and lens Convex Lens A virtual image

27. Object position, image position, and magnification real inverted image m < 1 Convex Lens real inverted image m >1 virtual erect image m >1

28. Types of lens Lens

29. Two lens systems Lens

30. Two lens systems (cont’d) Lens

31. Two lens systems (cont’d) Lens

32. Two lens systems (cont’d) Lens

33. Aberration sphere paraboloid

34. Chromatic aberration

35. Gravitational lens

36. Problem (focal length of a zoom lens) f2=-|f2| f1 ray bundle f1 r0 I’ Q r’0 r0 d x s2 d (variable)< f1 s’2 f Exercises Find the effective focal length f of the combination lens. Solution (a) (b) (c)