1. Mirrors, Plane and Spherical Spherical Refracting Surfaces
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. Is this kind of plane mirror possible?
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 and q is is the same angle at vertex P and vertex P’ the right triangles are congruent, and p = - q, also h = 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 For a thin lens in air, t is negligible
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. The SimpleMagnifier Measure angular magnifications
For reading distance
For infinite image

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)