Image Formation in Curved/Spherical Mirrors

ray diagramming of image formation in curved mirrors

1. Lesson 4: Image Formation Curved Mirrors Objectives: At the end of this lesson, the students should be able to Differentiate concave and convex mirrors. Describe the qualitative characteristics of images formed by curved mirrors. The Professional Development Service for Teachers is funded by the Department of Education and Skills under the National Development Plan

2. Terminologies used in Curved Mirrors The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan

3. M O R I R R

4. Curved Mirror The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan A mirror whose reflective surface is the side of the sphere

5. ELVIRA R. CONESE

6. Principal Axis The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan A line that intersects at the center of the curved mirror

7. C T V A U R R U E

8. Center of curvature The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan A point whose distance from the mirror is equal to the radius of the circle

9. Cal Cal Cal Cal .

10. Focal Point The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan A point between the center of curvature and vertex

11. SEPTEMBER, OCTOBER, NOVEMBER AND DECEMBER

12. Vertex The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan A point that intersects to the surface of the mirror.

13. 2 Types of Curved Mirrors The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan

14. Concave Mirror The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan Mirror whose reflective surface is the inner side of the circle.

15. Convex Mirror The Professional Development Service for Teachers is funded by the Department of Education and Science under the National Development Plan Mirror whose reflective surface is the outer side of the circle.

16. Basic differences between concave and convex mirrors Descriptions Concave Convex Reflective surface Inner surface Outer surface Also known as Converging mirror Diverging mirror Uses Make -up artists, dentists etc Convenience stores, security purposes and side mirrors.

17. Properties of an image Type Size Orientation Real Virtual Enlarged Reduced Same Upright Laterally Inverted Inverted (vertical)

18. Types of images Real - image appears in front of the mirror (could be projected onto a screen) Virtual - image appears behind the mirror

19. Virtual image

20. Sizes of images Enlarged - image is larger than the object Reduced - image is smaller than the object Same size - image is the same size as the object a) b) c)

21. Orientations of images Upright/Erect Inverted (vertical) Laterally Inverted image is right-side up image is upside-down image is flipped horizontally MIRROR MIRROR MIRROR

22. Concave Mirror- Part of a sphere reflective surface on inside C: the center point of the sphere r: radius of curvature (just the radius of the sphere) F: the focal point of the mirror (halfway between C and the mirror) f: the focal distance, f = r/2 r f • C • F

23. optical axis Concave Mirrors (caved in) • F Light rays that come in parallel to the optical axis reflect through the focal point Light rays that come in along the optical axis strike the mirror at 90 so reflect back along optical axis through the focal point.

24. ƒ = focal length u = object distance v = image distance

25. Ray Diagrams for Mirrors We can use three “ principal rays ” to construct images. In this example, the object is “outside” of F. Ray 1 is parallel to the axis and reflects through F. Ray 2 passes through F before reflecting parallel to the axis. Ray 3 passes through C and reflects back on itself. F C A fourth principal ray is the one directed at the vertex V. V

26. Principal axis Concave Mirror • F • c Image formed in a concave mirror object placed outside center of curvature Focus Centre of Curvature Object Image:- Between C and F, Inverted, smaller and real f v u

27. Object’s Location Image Location Orientation   Inverted vs. Upright Size larger, same size or smaller Type   Real vs. Virtual Beyond C       At C         Between C and F         At F         Between F and V        

28. Object’s Location Image Location Orientation   Inverted vs. Upright Size larger, same size or smaller Type   Real vs. Virtual Beyond C Between C and F inverted   smaller real  At C         Between C and F         At F         Between F and V        

29. Principal axis Concave Mirror • F • c Image formed in a concave mirror when object placed at center of curvature Focus Centre of Curvature Object Image: At C, Inverted, Same size and Real v f u

30. Principal axis Concave Mirror • F • c Image formed in a concave mirror when object placed at center of curvature Focus Centre of Curvature Object Image: At C, Inverted, Same size and Real v f u

31. Principal axis Concave Mirror • F • c Image formed in a concave mirror when object placed between center of curvature & focus Focus Centre of Curvature Object Image:- Beyond C, Inverted, larger and Real v f u

32. Principal axis Concave Mirror • F • c Image formed in a concave mirror when object placed at focus Focus Centre of Curvature Object Image: No image f u

33. Principal axis Concave Mirror • F • c Image formed in a concave mirror when object placed inside focus Focus Centre of Curvature Object Image:- Behind the mirror, upright, larger and virtual v f u

34. Object’s Location Image Location Orientation   Inverted vs. Upright Size larger, same size or smaller Type   Real vs. Virtual Beyond C Between C and F inverted   smaller real  At C Between C and F         At F         Between F and V        

35. Object’s Location Image Location Orientation   Inverted vs. Upright Size larger, same size or smaller Type   Real vs. Virtual Beyond C Between C and F inverted   smaller real  At C At C  inverted Same size  real  Between C and F         At F         Between F and V        

36. Magnification Equation m = magnification h i = image height h o = object height d i = image distance d o = object distance if the magnification is negative the image is inverted (upside down)

37. Sign Convention for Mirrors Quantity Positive (+) Negative (--) Object location (u) Object is in front of the mirror Object is behind the mirror Image location (v) Image is front mirror Image is behind of mirror Focal length (f) Mirror is concave Mirror is convex Magnification (M) Image is upright Image is inverted

38. Concave mirror Crosswire Lamp-box Screen u v TO FIND THE FOCAL LENGTH OF A CONCAVE MIRROR Procedure Get the approx. focal length of mirror by focusing distant object on screen – why? Place the lamp-box well outside the approximate focal length – why? Move the screen until a clear inverted image of the crosswire is obtained. Measure the distance u from the crosswire to the mirror, using the metre stick. Measure the distance v from the screen to the mirror. Calculate the focal length of the mirror using - - - - - - Repeat this procedure for different values of u. Calculate f each time and then find an average value.

39. Convex Mirrors Light rays that come in parallel to the optical axis reflect from the focal point. optical axis • F The focal point is considered virtual since sight lines, not light rays, go through it.

40. principal axis • C • F Convex Mirrors Image:- Behind the mirror, upright, smaller and virtual Focus Centre of Curvature Object v f u

41. Object’s Location Image Location Orientation Inverted vs. Upright Size larger, same size or smaller Type   Real vs. Virtual Beyond C Behind the mirror   upright  Smaller virtual At C         Between C and F         At F         Between F and V         Table : Qualitative Descriptions of Images Formed by Convex Mirrors

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