Geometric Optics

1. Geometric Optics Mirrors, Plane and Spherical Spherical Refracting Surfaces Thin Lenses Optical Instruments

2. General Definitions • O is the object or its coordinate • i is the image or its coordinate • p is the distance of the object to a mirror, refracting surface or lens • q (or i) is the distance of the image to a mirror , refracting surface or lens • h is the object height • h’ is the image height • lateral magnification is the ratio of image height to object height • an image is real if the light converges to form the image in space • an image is virtual if the light appears to come from a place where it cannot

3. Methods of chararacterizing the light wave • Wavefronts (3D surface of constant phase) • Huygen’s Principle • ray construction • lines perpendicular to wavefronts showing direction of motion of wave • the plane wave

4. Plane Mirrors Is this kind of plane mirror possible?

5. Plane Mirrors • Illustrating formation of an image by a plane mirror. • Since QR is common to both triangle PQR and triangle P’QR andqis is the same angle at vertex P and vertex P’ the right triangles are congruent, and p = - q, alsoh = h’ or the lateral magnification(M)is +1. • The image is upright, the same size and left-right reversed.

6. Images from Mirrors

7. Why spherical surfaces? • Easily made • Good approximation to more complex surfaces such as parabolic • Ubiquitous

8. Spherical Mirrors • Definitions for the following terms • Center of curvature (C) • Radius of curvature (R or r) • Principle Axis (or symmetry axis) • Vertex (V)

9. Spherical Mirrors Concave mirrors: real and virtual images Note: Rays 1,2, and 3 are called principle rays. See your text.

10. Spherical Mirrors Note: Ray through C retraces itself

11. Mirror Eq

12. Spherical Mirrors

13. Spherical Mirrors Focus and focal length

14. Spherical Mirrors Sign Convention

15. Spherical Mirrors Convex mirrors: virtual images only Note: Rays 1,2, and 3 are called principle rays. See your text.

16. Spherical Refracting Surfaces

17. Spherical Refracting Surfaces Substituting for q’s using the last two equations yields Assume paraxial rays Exterior angle of a triangle is equal to the sum of opposite interior angles

18. Spherical Refracting Surfaces Flat refracting surfaces and apparent depth

19. Thin Lenses • Two spherical refracting surfaces back to back • Thickness of lens is small (negligible)

20. Thin Lenses At the left surface For a thin lens in air, t is negligible and n1 is equal to 1 At the right surface And

21. Thin Lenses We find that when we look at the focus of the lens

22. Thin Lenses Sign convention

23. Thin Lenses Converging and Diverging Lenses

24. Thin Lenses Converging and Diverging Lenses Principle Rays Note: Rays 1,2, and 3 are called principle rays. See your text.

25. Thin Lenses Converging and Diverging Lenses

26. Thin Lenses Multiple Lens Systems How do you locate the final image? Where is the final image?

27. Lens Aberrations Spherical & chromatic Astigmatism Coma

28. The Camera Aperture size determined by number expressing it as a ratio of focal length to opening called f-number

29. The Eye The camera is modeled after the eye “Normal” reading distance is 25 cm Eye is about 2.5 cm in diameter Most of focusing is done by the cornea and vitreous humor behind the cornea

30. Myopia Correct for the far point Power of lens Lens powers add

31. Hyperopia • Correct for the near point

32. For reading distance For infinite image The SimpleMagnifier Measure angular magnifications

33. The Astronomical Telescope • Object is at infinity so image is at f • Measure angular magnification • Length of telescope light path is sum of focal lengths of objective and eyepiece

34. The Compound Microscope • Magnification is product of lateral magnification of objective and angular magnification of eyepiece • Note: Image is viewed at infinity

35. Plane Mirrors Multiple plane mirror images and optical illusions

36. Two Plane Mirrors in One What concept from the previous chapter is important to this illustration? Where is this design used?

37. Spherical Aberration Aberration is reduced by considering rays close to the optic axis • Rays are called paraxial rays (will be used for all spherical surfaces)