1. Chapter 16 EM Spectrum Reflection Flat Mirrors Curved Mirrors
Geometric optics
Chapter 16
EM Spectrum
Reflection
Flat Mirrors
Curved Mirrors

2. Optics Optics: the study of light & its behavior
Light has been described as a particle, as a wave, and a combination of the two
Geometric optics: deals with light as a ray or beam
Reflection, mirrors, refraction, lenses
Physical optics: deals with light as a wave
Interference, diffraction, polarization, color, spectroscopy

3. Light
When most people think of light, they think of the light that they can see
The electromagnetic spectrum includes more than visible light
An electromagnetic wave consists of electric and magnetic field waves at right angles to each other

4. The Electromagnetic Spectrum

5. The Electromagnetic Spectrum

6. Electromagnetic Waves
Light is a wave composed of oscillating electric & magnetic fields at right angles to the direction of wave propagation
What type of waves are EM waves?
What causes these fields?

7. Electromagnetic Waves
Light is a wave composed of oscillating electric & magnetic fields at right angles to the direction of wave propagation
What type of waves are EM waves?
transverse
What causes these fields?
a vibrating charge

8. Electromagnetic Waves
EM waves are distinguished by their different frequencies and wavelengths
You should have a sketch of the spectrum in your notes, including the relationship between wavelength, frequency & energy… and yes, you should know the order of the spectrum as well

9. Electromagnetic Waves
ALL EM waves move at the speed of light, c, which is ×108 m/s
For our calculations, c = 3.00 ×108 m/s
The relationship between frequency, wavelength & speed we used in waves & sound unit holds true for light waves
𝒄=𝒇λ
speed of light = frequency x wavelength

10. Electromagnetic Waves
Waves can be approximated as rays
The broad crest of a wave that is perpendicular to the wave’s motion is made up of a line of water particles
Another line of particles forms a trough in the wave
In any type of wave, these lines of particles are called wave fronts

11. Electromagnetic Waves
All the points on the wave front of a plane wave can be treated as point sources
Each of these point sources produces a circular or spherical secondary wave, a wavelet
A line that is tangent to each of these wavelets at some later time determines the new position of the initial wave front
Huygens’ principle
Treat the propagating wave as a straight line perpendicular to the wave front
This line is called a ray
This simplification = ray approximation

12. Reflection
Light traveling through a uniform source always travels in a straight line
When light encounters a different substance, its path will change
Reflection = the change in direction of light
A good mirror can reflect about 90% of the incident light
No surface is a perfect reflector

13. Reflection The texture of a surface affects reflection
Diffuse reflection
Rough, textured surface  reflection in many directions
Specular reflection
Smooth surface  reflection in one direction

14. Reflection
Snell’s Law: Angle of incidence (incoming) = angle of reflection (θ = θ’) (law of reflection) Line perpendicular to reflecting surface = normal
90 - θ
90 - θ

15. Flat Mirrors Simplest mirror
If an object is placed at a distance in front of a flat mirror and light is bounced off it, light rays spread out from the object and reflect from the mirror’s surface
Rays appear to come from a location on the other side of the mirror
Object’s image is said to be at this location behind the mirror

16. Image of object is same size as object
Flat Mirrors
Object distance from mirror = p
Image distance = q
In a flat mirror:
p = q
Image of object is same size as object

17. Flat Mirrors
Image formed by rays that appear to come from the image point behind the mirror (but never really do) = virtual image Flat mirrors always form virtual images, which always appear as if they are behind the surface of the mirror Virtual images can never be displayed on a physical surface

18. Image location can be predicted with ray diagrams

19. Curved Mirrors

20. Curved Mirrors Concave spherical mirrors Convex spherical mirrors
Inwardly curved mirrored portion of a sphere
Converges incoming light rays to form real images (can also virtual images)
Light rays actually intersect at a single point & can be displayed on a surface
Convex spherical mirrors
Outwardly curved mirrored portion of a sphere
Diverges incoming light rays to form virtual images
Rays appear to intersect at a point behind mirror

21. Curved Mirrors
Principal axis (PA) = line that extends infinitely from center of mirrors surface through C
C = center of curvature
R = radius of curvature
F = focal point (midway between R and V)
V = vortex = center of mirror
f = focal length
q = image distance
p = object distance V

22. The Mirror Equation 1 𝑝 + 1 𝑞 = 2 𝑅
If object is very far from mirror, p is great enough compared with R that 1/p is essentially 0:
0+ 1 𝑞 = 2 𝑅  q = R/2
* image forms halfway between C & V
* image point in this case = F (focal point)
* when image is at F, the image distance, q, is called the focal length, f  f = R/2

23. Virtual Images Thurs-Sun Chap 17-19 Read/Notes
Virtual Images are basically images which cannot be visually projected on a screen.
If this box gave off light, we could project an image of this box on to a screen provided the screen was on the SAME SIDE as the box.
You would not be able to project the image of the vase or your face in a mirror on a screen, therefore it is a virtual image.
CONCLUSION: VIRTUAL IMAGES are ALWAYS on the OPPOSITE side of the mirror relative to the object.

24. Real Image
Real Images are ones you can project on to a screen.
For MIRRORS they always appear on the SAME SIDE of the mirror as the object.
The characteristics of the image, however, may be different from the original object. These characteristics are:
SIZE (reduced,enlarged,same size)
POSITION (same side, opposite side)
ORIENTATION (right side up, inverted)
object
image
What if the mirror isn’t flat?

25. Spherical Mirrors – Concave & Convex
Also called DIVERGING mirror
Also called CONVERGING mirror

26. Converging (Concave) Mirror
A converging mirror is one that is spherical in nature by which it can FOCUS parallel light rays to a point directly in front of its surface. Every spherical mirror can do this and this special point is at a “fixed” position for every mirror. We call this point the FOCAL POINT. To find this point you MUST use light from “infinity”
Light from an “infinite” distance, most likely the sun.

27. Converging (Concave) Mirror
Since the mirror is spherical it technically has a CENTER OF CURVATURE, C. The focal point happens to be HALF this distance.
We also draw a line through the center of the mirror and call it the PRINCIPAL AXIS.

28. Ray Diagram
A ray diagram is a pictorial representation of how the light travels to form an image and can tell you the characteristics of the image.
object C f
Principal axis
Rule One: Draw a ray, starting from the top of the object, parallel to the principal axis and then through “f” after reflection.

29. Ray Diagrams object C f Principal axis
Rule Two: Draw a ray, starting from the top of the object, through the focal point, then parallel to the principal axis after reflection.

30. Ray Diagrams object C f Principal axis
Rule Three: Draw a ray, starting from the top of the object, through C, then back upon itself.
What do you notice about the three lines?
THEY INTERSECT
The intersection is the location of the image.

31. Ray Diagram – Image Characteristics
object C f
Principal axis
After getting the intersection, draw an arrow down from the principal axis to the point of intersection. Then ask yourself these questions:
Is the image on the SAME or OPPOSITE side of the mirror as the object?
Same, therefore it is a REAL IMAGE.
Is the image ENLARGED or REDUCED?
Is the image INVERTED or RIGHT SIDE UP?

32. The Mirror Equation 𝟏 𝒑 + 𝟏 𝒒 = 𝟏 𝒇 p = object distance
q = image distance
f = focal length

33. The Mirror/Lens Equation
Is there any OTHER way to predict image characteristics besides the ray diagram? YES!
One way is to use the MIRROR/LENS equation to CALCULATE the position of the image.

34. Example -10 cm VIRTUAL (opposite side) Enlarged Upright 2x
Assume that a certain concave spherical mirror has a focal length of 10.0 cm. Locate the image for an object distance of 5 cm and describe the image’s characteristics.
-10 cm
Characteristics?
VIRTUAL (opposite side)
Enlarged
Upright 2x

35. Mirror/Lens Equation
Assume that a certain concave spherical mirror has a focal length of 10.0 cm. Locate the image for an object distance of 25 cm and describe the image’s characteristics.
16.67 cm
What does this tell us? First we know the image is BETWEEN “C” & “f”. Since the image distance is POSITIVE the image is a REAL IMAGE.
Real image = positive image distance
Virtual image = negative image distance
What about the size and orientation?

36. Magnification (M) Relates image and object sizes 𝑴= 𝒉′ 𝒉 =− 𝒒 𝒑
M = ratio of the height of an image to the object’s actual height
M = the negative of the ratio of the image distance to the object distance
If image is smaller than object, M < 1
If image is larger than object, M > 1
𝑴= 𝒉′ 𝒉 =− 𝒒 𝒑

37. Magnification 𝑴= 𝒉′ 𝒉 =− 𝒒 𝒑
If image is in front of the mirror (+), M is (-) and image is inverted (upside down)
Real images
If image is behind the mirror (-), M is (+) and image is upright
Virtual images

38. Magnification Equation
To calculate the orientation and size of the image we use the MAGNIFICATION EQUATION.
Here is how this works:
If we get a POSITIVE magnification, the image is UPRIGHT.
If we get a NEGATIVE magnification, the image is INVERTED
If the magnification value is GREATER than 1, the image is ENLARGED.
If the magnification value is LESS than 1, the image is REDUCED.
If the magnification value is EQUAL to 1, the image is the SAME SIZE as the object.
Using our previous data we see that our image was INVERTED, and REDUCED.

39. Bellringer 4/20/18
2. The same Star Wars action figure, 8.0 cm tall, is placed 6.0 cm in front of a convex mirror with a focal length of cm. Where is the image in this case, and what are the image characteristics?
A Star Wars action figure, 8.0 cm tall, is placed 23.0 cm in front of a concave mirror with a focal length of 10.0 cm. Where is the image? How tall is the image? What are the characteristics of the image?

40. The Mirror Equation
The region in which light rays reflect and form real images is called the front side of the mirror
The other side, where light rays do not exist, and where virtual images are formed = back side
Mirror usually drawn so that the front side is to the left and back side is to the right
Front side = (+) distances for p & q
Back side = (-) distances for q
Focal length always (+) for concave mirrors
Object and image heights (h and h’, respectively) are (+) when both are above principal axis, and are (-) when either is below the principal axis

41. Rules for Drawing Ray Diagrams
Draw to scale (use a ruler!)
Follow guidelines for reference rays
Ray
Line drawn from object  mirror
Line drawn from mirror  image after reflection 1
Parallel to principal axis
Through focal point (F) 2 3
Through center of curvature (C)
Back along itself through C

42. Case 1 Configuration of object: at infinity Image is: real smaller
inverted
Image location: at focal point (F)

43. Case 2 Configuration of object: outside C Image is: real smaller
inverted
Image location: between C & F

44. Case 3 Configuration of object: at C Image is: real same size inverted
Image location: at C

45. ** rays 1 & 2 are mislabeled in this diagram… switch them
Case 4
Configuration of object: between C and F
Image is:
real
larger
inverted
Image location: behind C
** rays 1 & 2 are mislabeled in this diagram… switch them

46. Case 5
Configuration of object: at F
NO IMAGE

47. Case 6 Configuration of object: very close to mirror, inside F
Image is:
virtual
larger
upright
Image location: behind mirror

48. Convex Spherical Mirrors
Incoming light rays diverge after reflection as though they were coming from some point behind the mirror
What types of images are produced?

49. Convex Spherical Mirrors
Focal point and center of curvature behind mirror’s surface
Virtual, smaller, upright images form where three rays appear to intersect
Magnification always less than one

50. Convex Spherical Mirrors
Side-view mirror on passenger’s side of car
In stores
Intersections of busy hallways/streets

51. Example 2
An upright pencil is placed in front of a convex spherical mirror with a focal length of 8.00 cm. An upright image 2.50 cm tall is formed 4.44 cm behind the mirror. Find the position of the object, the magnification of the image, and the height of the pencil.

52. solution Convex Mirrors Given: Unknown: Using mirror equation
Because the mirror is convex, the focal length is negative. The image is behind the mirror, so q is also negative.
f = –8.00 cm q = –4.44 cm h’ = 2.50 cm
Unknown:
p = ? h = ?
Using mirror equation
1 𝑓 = 1 𝑝 + 1 𝑞
1 −8 = 1 𝑝 + 1 −4.44
Solve for p
1 −8 − 1 −4.44 = 1 𝑞
1 10 = 1 𝑝
p=.1 cm

53. solution
Using magnification equation M=-q/p M=.444 M=h’/h H=h’/m=5.63 cm

54. Spherical Aberration
Certain rays in ray diagrams do not intersect at the image point
Especially rays that reflect at the mirror’s surface far from the PA
Rays that reflect at points far from the PA of the mirror converge at slightly different points, producing a blurred image

55. Parabolic Mirrors
Segments of a paraboloid whose inner surface is a mirror
All rays parallel to the PA converge at the focal point regardless of where on the mirror they reflect
Ideal for flashlights & headlights
Used in reflecting telescopes