Geometric Optics: Mirrors, Light, and Image Formation

Delve into the world of geometric optics as you explore how light rays form images with optical instruments, understand the ray model of light, and discover the laws of reflection and refraction. From reflection and refraction on plane mirrors to key terms like specular reflection and virtual images, this comprehensive guide provides insights into image formation by a plane mirror through insightful diagrams and explanations.

• Geometric Optics
• Mirrors
• Light
• Image Formation
• Reflection

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1. Geometric Optics Mirrors, light, and image formation

2. Geometric Optics Understanding images and image formation, ray model of light, laws of reflection and refraction, and some simple geometry and trigonometry The study of how light rays form images with optical instruments

3. Reflection and refraction on plane mirrors REFLECTION AND REFRACTION AT A PLANE SURFACE

4. Key terms Anything from which light rays radiate Object Anything from which light rays radiate that has no physical extent Point object Real objects with length, width, and height Extended objects

5. Key terms Specular reflection Diffused reflection Reflection on a plane surface where reflected rays are in the same directions Relfection on a rough surface

6. Key terms Virtual image Real image Image formed if the outgoing rays actually pass through the image point Image formed if the outgoing rays don t actually pass through the image point

7. Image formation by a Plane mirror

8. Image formation by a Plane mirror a diagram that traces the path that light takes in order for a person to view a point on the image of an object Ray Diagrams suggests that in order to view an image of an object in a mirror, a person must sight along a line at the image of the object. Line of Sight Principle

10. Reflection at a Plane Surface

11. Image formation by a Plane mirror M M V s s

12. Image formation by a Plane mirror M is the object and M is the virtual image Ray MV is incident normally to the plane mirror and it returns along its original path s= object distance s = image distance s=-s

13. Image formation by a Plane mirror Sign rules For the object distance: When the object is on the same side of the reflecting or the refracting surface as the incoming light, s is positive For the image distance: When the image is on the same side of the reflecting or the refracting surface as the outgoing light, s is positive

14. Image of an extended object Q Q V y y M M s s V

15. Image of an extended object Lateral magnification Ratio of image height to object height M=y /y Image is erect m for a plane mirror is always +1 Reversed means front-back dimension is reversed

16. Reflection on Concave and Convex mirrors REFLECTION AT A SPHERICAL SURFACE

17. Reflection at a Concave Mirror V C P P

18. Reflection at a Concave Mirror Radius of curvature R Center of curvature The center of the sphere of which the surface is a part C Vertex The point of the mirror surface V CV Optic axis

19. Graphical Methods for Mirrors IMAGE FORMATION ON SPHERICAL MIRRORS

20. Graphical Method Consists of finding the point of intersection of a few particular rays that diverge from a point of the object and are reflected by the mirror Neglecting aberrations, all rays from this object point that strike the mirror will intersect at the same point

21. Graphical Method For this construction, we always choose an object point that is not on the optic axis Consists of four rays we can usually easily draw, called the principal rays

22. Graphical Method A ray parallel to the axis, after reflection passes through F of a concave mirror or appears to come from the (virtual) F of a convex mirror A ray through (or proceeding toward) F is reflected parallel to the axis A ray along the radius through or away from C intersects the surface normally and is reflected back along its original path A ray to V is reflected forming equal angles with the optic axis

23. Object is at F

24. Object is between F and Vertex

25. Object is at C

26. Object is between C and F

27. Positions of objects for concave mirrors

28. Image formation by concave mirrors Position of object Position of image Character of image Real, inverted, reduced Real, inverted, same size Real, inverted, enlarged No image Virtual, upright, enlarged Virtual, upright, same size Beyond C Between F and C At C At C Between C and F Beyond C At F At infinity Between F and Vertex Beyond the vertex At V At V

29. Reflection at a Concave Mirror If dec, i is nearly parallel Rays nearly parallel or close to R Paraxial rays

30. Reflection at a Concave Mirror If inc, P is close to V Image is smeared out Spherical Aberration

31. Reflection at a Concave Mirror V F C s at infinity s = R/2

32. Reflection at a Concave Mirror All reflected rays converge on the image point Converging mirror If R is infinite, the mirror becomes plane

33. Reflection at a Concave Mirror The incident parallel rays converge after reflecting from the mirror They converge at a F at a distance R/2 from V f= R/2 f is the focal length, distance from the vertex to the focal point F is Focal point, where the rays are brought to focus

34. Reflection at a Concave Mirror V F C s at infinity s= R/2

35. Reflection at a Concave Mirror The object is at the focal point 1/s+ 1/s = 1/f Object image relation, spherical mirror s=f=R/2 1/s =0; s at infinity 1/s +1/s = 2/R

36. Image of an Extended Object Lateral magnification m= y /y Lateral m= y /y= -s /s magnification for spherical mirrors

37. Reflection at a Convex Mirror F C s or s= R/2 s or s at infinity

38. Image formation on spherical mirrors Sign rules For the object distance: When the object is on the same side of the reflecting or the refracting surface as the incoming light, s is positive; otherwise, it is negative

39. Image formation on spherical mirrors Sign rules For the image distance: When the image is on the same side of the reflecting or the refracting surface as the outgoing light, s is positive; otherwise, it is negative

40. Image formation on spherical mirrors Sign rules: 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 curvature is positive, otherwise negative

41. Reflection at a Convex Mirror The convex side of the spherical mirror faces the incident light C is at the opposite side of the outgoing rays, so R is neg. All reflected rays diverge from the same point Diverging mirror

42. Reflection at a Convex Mirror Incoming rays are parallel to the optic axis and are not reflected through F s is positive, s is negative Incoming rays diverge, as though they had come from point F behind the mirror F is a virtual focal point

43. Refraction at spherical interface REFRACTION AT A SPHERICAL SURFACE

44. Refraction at a Spherical Surface C V

45. Refraction at a Spherical Surface Object-image relation, spherical refracting surface na/s + nb/s = (nb-na)/R na/s + nb/s =0 At a plane refracting surface Lateral magnification, spherical refracting surface m=y /y= -(nas /nbs)

46. Biconcave and biconvex thin lenses GRAPHICAL METHOD FOR LENSES

50. Lenses

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