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Chapter 31: Images and Optical Instruments Reflection at a plane surface  Image formation P P’ The reflected rays entering eyes look as though they had.

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Presentation on theme: "Chapter 31: Images and Optical Instruments Reflection at a plane surface  Image formation P P’ The reflected rays entering eyes look as though they had."— Presentation transcript:

1 Chapter 31: Images and Optical Instruments Reflection at a plane surface  Image formation P P’ The reflected rays entering eyes look as though they had come from image P’. Light rays radiate from a point object at P in all directions. virtual image

2 Reflection and refraction at a plane surface  Image formation

3 Reflection and refraction at a plane surface  Image formation i (or s’) is the image distance s is the object distance: |s| =|i| Sign Rules: (1)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 ( or 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 Reflection at a plane surface  Image formation Multiple image due to multiple Reflection by two mirrors h h’ m = h’/h=1 lateral magnification image is erect image is virtual

5 Reflection at a plane surface  Image formation When a flat mirror is rotated, how much is the image rotated?

6 Reflection at a spherical mirror  Concave and convex mirror

7 Reflection at a spherical mirror  Focal points at concave and convex mirror 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.

8 Reflection at a spherical mirror  Focal points at a concave mirror h d object image If s’

9 Reflection at a spherical mirror  Image of an extended object at a concave mirror 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 real image

10 Reflection at a spherical mirror  Magnification of image at a concave mirror h h’ When s,s’ >0, m<0 inverted s/s’ 0 upright or erect

11 Reflection at a spherical mirror  Example with a concave mirror real image virtual image

12 Reflection at a spherical mirror  Example with a concave mirror

13 Reflection at a spherical mirror  Image at a convex mirror ss’ f f R s positive s’ negative (virtual image) R negative f negative

14 Reflection at a spherical mirror  Magnification of image at a convex mirror s’ For a convex mirror f < 0 m > 1 magnified m < 1 minimized m > 0 image upright m < 0 image inverted

15 Refraction at a spherical surface  Refraction at a convex spherical surface For small angles     

16 Refraction at a spherical surface  Refraction at a concave 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.

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

18 Refraction at a spherical surface  Example of a convex surface |s’|

19 Refraction at a spherical surface  Example of a concave surface |s’|

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

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

22 Convex Lens  Sign rules for convex and concave lens: Sign Rules: (1)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 (or s’) 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.

23 Convex Lens  Lens-makers (thin lens) formula surface 1 surface 2 Image due to surface 1: s’ 1 becomes source s 2 for surface 2: s 1 = s and s’ 2 = s’: s’ Parallel rays (s=inf.) w.r.t. the axis converge at the focal point R 1 >0R 2 <0

24 Convex Lens  Magnification s’ same as for mirrors

25 Convex Lens  Object between the focal point and lens A virtual image

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

27 Lens  Types of lens

28 Lens  Two lens systems

29 Lens  Two lens systems (cont’d)

30 Lens  Two lens systems (cont’d)

31 Lens  Two lens systems (cont’d)

32 Eyes  Anatomy of eye

33 Eyes  Near- and far-sightedness and corrective lenses farsightedness nearsightedness

34 Angular size h d In general the minimum distance d=d min ~25 cm at which an eye can see image of an object comfortably and clearly.

35 Magnifying glass whenbut for human eye. the minimum distance at which an eye can see image of an object comfortably and clearly. virtual image s’ the eye is most relaxed s ii hihi h

36 Microscope small Object is placed near F 1 (s 1 ~f 1 ). Image by lens1 is close to the focal point of lens2 at F 2. magnifier image ang. size ii

37 Refracting telescope angular size of image by lens2; eye is close to eyepiece image height by lens1 at its focal point Image by lens1 is at its focal point which is the focal point of lens 2 image distance after lens1 magnifier

38 Reflecting telescope

39 Aberration sphereparaboloid

40 Chromatic aberration

41 Gravitational lens

42 Exercises Problem 1 Solution x/2 (h-x)/2 h-x x What is the size of the smallest vertical plane mirror in which a woman of height h can see her full-length? The minimum length of mirror for a woman to see her full height h Is h/2 as shown in the figure right.

43 Exercises Problem 2 (focal length of a zoom lens) I’ r0r0 Q f1f1 f 2 =-|f 2 | r’ 0 d (variable)f 1 -d

44 Exercises Problem 2 (focal length of a zoom lens) I’ r0r0 Q f1f1 f 2 =-|f 2 | r’ 0 d (variable)

45 Exercises Problem 2 (focal length of a zoom lens) I’ r0r0 Q f1f1 f 2 =-|f 2 | r’ 0 d (variable)


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