1. College Physics by Serway and Faughn Chapter 23 and 25
Mirrors and Lenses

2. Notation for Mirrors and Lenses
The object distance is the distance from the object to the mirror or lens
Denoted by p
The image distance is the distance from the image to the mirror or lens
Denoted by q
The lateral magnification of the mirror or lens is the ratio of the image height to the object height
Denoted by M

3. Types of Images for Mirrors and Lenses
A real image is one in which light actually passes through the image point
Real images can be displayed on screens
A virtual image is one in which the light does not pass through the image point
The light appears to diverge from that point
Virtual images cannot be displayed on screens

4. More About Images
To find where an image is formed, it is always necessary to follow at least two rays of light as they reflect from the mirror

5. Atmospheric Refraction
There are many interesting results of refraction in the atmosphere
Sunsets
Mirages

6. Atmospheric Refraction and Sunsets
Light rays from the sun are bent as they pass into the atmosphere
It is a gradual bend because the light passes through layers of the atmosphere
Each layer has a slightly different index of refraction
The Sun is seen to be above the horizon even after it has fallen below it

7. Atmospheric Refraction and Mirages
A mirage can be observed when the air above the ground is warmer than the air at higher elevations
The rays in path B are directed toward the ground and then bent by refraction
The observer sees both an upright and an inverted image

8. Thin Lenses
A thin lens consists of a piece of glass or plastic, ground so that each of its two refracting surfaces is a segment of either a sphere or a plane
Lenses are commonly used to form images by refraction in optical instruments

9. Thin Lens Shapes These are examples of converging lenses
They have positive focal lengths
They are thickest in the middle

10. More Thin Lens Shapes These are examples of diverging lenses
They have negative focal lengths
They are thickest at the edges

11. Focal Length of Lenses
The focal length, ƒ, is the image distance that corresponds to an infinite object distance
This is the same as for mirrors
A thin lens has two focal points, corresponding to parallel rays from the left and from the right
A thin lens is one in which the distance between the surface of the lens and the center of the lens is negligible

12. Focal Length of a Converging Lens
The parallel rays pass through the lens and converge at the focal point
The parallel rays can come from the left or right of the lens

13. Focal Length of a Diverging Lens
The parallel rays diverge after passing through the diverging lens
The focal point is the point where the rays appear to have originated

14. Lens Equations
The geometric derivation of the equations is very similar to that of mirrors

15. Lens Equations
The equations can be used for both converging and diverging lenses
A converging lens has a positive focal length
A diverging lens has a negative focal length

16. Sign Conventions for Thin Lenses
Quantity
Positive When
Negative When
Object location (p)
Object is in front of the lens
Object is in back of the lens
Image location (q)
Image is in back of the lens
Image is in front of the lens
Image height (h’)
Image is upright
Image is inverted
R1 and R2
Center of curvature is in back of the lens
Center of curvature is in front of the lens
Focal length (f)
Converging lens
Diverging lens

17. Ray Diagrams for Thin Lenses
Ray diagrams are essential for understanding the overall image formation
Three rays are drawn
The first ray is drawn parallel to the first principle axis and then passes through (or appears to come from) one of the focal lengths
The second ray is drawn through the center of the lens and continues in a straight line
The third ray is drawn from the other focal point and emerges from the lens parallel to the principle axis
There are an infinite number of rays, these are convenient

18. Ray Diagram for Converging Lens, p > f
The image is real
The image is inverted

19. Ray Diagram for Converging Lens, p < f
The image is virtual
The image is upright

20. Ray Diagram for Diverging Lens
The image is virtual
The image is upright

21. A plastic sandwich bag filled with water can act as a crude converging lens in air. If the bag is filled with air and placed under water, is the effective lens (a) converging or (b) diverging?
QUICK QUIZ 23.4

22. QUICK QUIZ 23.4 ANSWER
(b). In this case, the index of refraction of the lens material is less than that of the surrounding medium. Under these conditions, a biconvex lens will be divergent.

23. QUICK QUIZ 23.5
In the figure below, the blue object arrow is replaced by one that is much taller than the lens. How many rays from the object will strike the lens?

24. QUICK QUIZ 23.5 ANSWER
Although a ray diagram only uses 2 or 3 rays (those whose direction is easily determined using only a straight edge), an infinite number of rays leaving the object will always pass through the lens.

25. QUICK QUIZ 23.6
An object is placed to the left of a converging lens. Which of the following statements are true and which are false? (a) The image is always to the right of the lens. (b) The image can be upright or inverted. (c) The image is always smaller or the same size as the object. Justify your answers with ray diagrams.

26. QUICK QUIZ 23.6 ANSWER
(a) False. A virtual image is formed on the left side of the lens if p < f. (b) True. An upright, virtual image is formed when p < f, while an inverted, real image is formed when p > f. (c) False. A magnified, real image is formed if 2f > p > f, and a magnified, virtual image is formed if p > f.

27. Problem Solving Strategy
Be very careful about sign conventions
Do lots of problems for practice
Draw confirming ray diagrams

28. Combinations of Thin Lenses
The image produced by the first lens is calculated as though the second lens were not present
The light then approaches the second lens as if it had come from the image of the first lens
The image of the first lens is treated as the object of the second lens
The image formed by the second lens is the final image of the system

29. Combination of Thin Lenses, 2
If the image formed by the first lens lies on the back side of the second lens, then the image is treated at a virtual object for the second lens
p will be negative
The overall magnification is the product of the magnification of the separate lenses

30. Combination of Thin Lenses, example

31. Lens and Mirror Aberrations
One of the basic problems is the imperfect quality of the images
Largely the result of defects in shape and form
Two common types of aberrations exist
Spherical aberration
Chromatic aberration

32. Spherical Aberration
Results from the focal points of light rays far from the principle axis are different from the focal points of rays passing near the axis
For a mirror, parabolic shapes can be used to correct for spherical aberration

33. Chromatic Aberration
Different wavelengths of light refracted by by a lens focus at different points
Violet rays are refracted more than red rays
The focal length for red light is greater than the focal length for violet light
Chromatic aberration can be minimized by the use of a combination of converging and diverging lenses

34. Chapter 25
Optical Instruments

35. Optical Instruments
Analysis generally involves the laws of reflection and refraction
Analysis uses the procedures of geometric optics
To explain certain phenomena, the wave nature of light must be used

36. Diopters
Optometrists and ophthalmologists usually prescribe lenses measured in diopters
The power of a lens in diopters equals the inverse of the focal length in meters
P = 1/ƒ

37. Simple Magnifier
A simple magnifier consists of a single converging lens
This device is used to increase the apparent size of an object
The size of an image formed on the retina depends on the angle subtended by the eye

38. The Size of a Magnified Image
When an object is placed at the near point, the angle subtended is a maximum
The near point is about 25 cm
When the object is placed near the focal point of a converging lens, the lens forms a virtual, upright, and enlarged image

39. Angular Magnification
Angular magnification is defined as
The angular magnification is at a maximum when the image formed by the lens is at the near point of the eye
q = - 25 cm
Calculated by

40. Magnification by a Lens
With a single lens, it is possible to achieve angular magnification up to about 4 without serious aberrations
With multiple lens, magnifications of up to about 20 can be achieved
The multiple lens can correct for aberrations

41. Compound Microscope A compound microscope consists of two lenses
Gives greater magnification than a single lens
The objective lens has a short focal length, ƒo<1 cm
The ocular lens (eyepiece) has a focal length, ƒe of a few cm

42. Compound Microscope, cont
The lens are separated by a distance L
L is much greater than either focal length
The approach to analysis is the same as for any two lenses in a row
The image formed by the first lens becomes the object for the second lens
The image seen by the eye, I2, is virtual, inverted and very much enlarged

43. Magnifications of the Compound Microscope
The lateral magnification of the microscope is
The angular magnification of the eyepiece of the microscope is
The overall magnification of the microscope is the product of the individual magnifications

44. Other Considerations with a Microscope
The ability of an optical microscope to view an object depends on the size of the object relative to the wavelength of the light used to observe it
For example, you could not observe an atom (d  0.1 nm) with visible light (λ 500 nm)

45. Telescopes Two fundamental types of telescopes
Refracting telescope uses a combination of lens to form an image
Reflecting telescope uses a curved mirror and a lens to form an image
Telescopes can be analyzed by considering them to be two optical elements in a row
The image of the first element becomes the object of the second element

46. Refracting Telescope
The two lenses are arranged so that the objective forms a real, inverted image of a distance object
The image is near the focal point of the eyepiece
The two lenses are separated by the distance ƒo + ƒe which corresponds to the length of the tube
The eyepiece forms an enlarged, inverted image of the first image

47. Angular Magnification of a Telescope
The angular magnification depends on the focal lengths of the objective and eyepiece
Angular magnification is particularly important for observing nearby objects
Very distance objects still appear as a small point of light

48. Disadvantages of Refracting Telescopes
Large diameters are needed to study distant objects
Large lenses are difficult and expensive to manufacture
The weight of large lenses leads to sagging which produces aberrations

49. Reflecting Telescope
Helps overcome some of the disadvantages of refracting telescopes
Replaces the objective lens with a mirror
The mirror is often parabolic to overcome spherical aberrations
In addition, the light never passes through glass
Except the eyepiece
Reduced chromatic aberrations

50. Reflecting Telescope, Newtonian Focus
The incoming rays are reflected from the mirror and converge toward point A
At A, a photographic plate or other detector could be placed
A small flat mirror, M, reflects the light toward an opening in the side and passes into an eyepiece

51. Examples of Telescopes
Reflecting Telescopes
Largest in the world are 10 m diameter Keck telescopes on Mauna Kea in Hawaii
Largest single mirror in US is 5 m diameter on Mount Palomar in California
Refracting Telescopes
Largest in the world is Yerkes Observatory in Wisconsin
Has a 1 m diameter