1. Introduction to Mirrors
SPH3UW: OPTICS I
Introduction to Mirrors 1

2. Light incident on an object
Absorption
Reflection (bounces)**
See it
Mirrors
Refraction (bends)
Lenses
Often some of each
Everything true for wavelengths << object size

3. qi = qr Reflection Angle of incidence = Angle of reflection
(Angles between light beam and normal) qi qr
Before this slide, bounce pass basket ball

4. We know object’s location by the direction the light rays come from.
Object Location
Light rays from sun bounce off object and go in all directions
Some of the rays hit your eyes
We know object’s location by the direction the light rays come from.
Color: some light is absorbed by object before bouncing off.

5. Reflection from a Plane Mirror
The angle of incidence equals the angle of reflection. This assumes the surface is perfectly smooth.

6. Diffuse Reflection
When the surface is rough, the surface at any point makes some angle with respect to the horizontal. The angle of incidence still equals the angle of reflection.

7. Plane Mirrors
In the left hand picture with a rough surface, you can place your eye anywhere and you will see some reflected rays. On the right hand side, you eye has to be in the correct position to see the reflected light. This is called specular reflection.

8. Plane Mirrors
A plane mirror provides the opportunity to fool you by making your eye and brain perceive an image.

9. Plane Mirrors
The image appears to be the same distance behind the mirror as the object is in front of the mirror.

10. Plane Mirrors
The image is called a virtual image because if you placed a piece of paper at the image location, you wouldn’t see any light.

11. Plane Mirror All you see is what reaches your eyes Image Object
You think object’s location is where rays appears to come from. qr qi
All rays originating from peak will appear to come from same point behind mirror!
Image
Object

12. How to Draw the Image in a Plane Mirror
(1) Draw first ray perpendicular to mirror qi =00= qr
(2) Draw second or third ray at angle. qi = qr
(3) Where the extended lines appear to intersect (a distance d behind mirror) is the image location.
Light rays don’t really converge there, so it’s a “Virtual Image”
Virtual: No light actually gets here.
Here can do cool light with ½ silvered mirror demo. qr qi qr d qi

13. How Big a Mirror?
0.80 m

14. Question
Why do ambulances have “AMBULANCE” written backwards?

15. So you can read it in your rear-view mirror!
Solution
Might change Virtual Image definition “Light rays don’t actually intersect at image location.”
So you can read it in your rear-view mirror!

16. Question
Can you see Fido’s tail in mirror?
mirror
(You)
(Fido)

17. No! Solution Can you see Fido’s tail in mirror? (You) (Fido) mirror
You need light rays from the tail to bounce off mirror and reach your eye!
(You)
(Fido)

18. ACT: Plane Mirrors
You are standing in front of a short flat mirror which is placed too high, so you can see above your head, but only down to your knees. To see your shoes, you must move:
(1) closer to the mirror.
(2) further from the mirror.
(3) to another mirror.

19. ACT: Plane Mirrors
You are standing in front of a short flat mirror which is placed too high, so you can see above your head, but only down to your knees. To see your shoes, you must move:
(1) closer to the mirror.
(2) further from the mirror.
(3) to another mirror.
Changing distance doesn’t change what you see of yourself

20. Two Mirrors
How many images of money will you see (not including the actual money)?

21. Two Mirrors
How many images of money will you see (not including the actual money)? 2 1 3

22. Curved mirrors • • A Spherical Mirror: section of a sphere.
principal axis
light ray •
Concave mirror R C R
Convex mirror
principal axis
light ray R C •
C = Center of Curvature
In front of concave mirror
Behind convex mirror.

23. Understanding
An organic chemistry student accidentally drops a glass marble into a silver nitrate mirroring solution, making the outside of the marble reflective.
What kind of mirror is this?
(1) concave
(2) convex
(3) flat

24. Concave Mirror Focus Principal Axis f=R/2
Rays are bent towards the principal axis.
Rays parallel to principal axis and near the principal axis (“paraxial rays”) all reflect so they pass through the “Focus” (F).
The distance from F to the center of the mirror is called the “Focal Length” (f).

25. Understanding
What kind of spherical mirror can be used to start a fire?
concave
convex
How far from the paper to be ignited should the mirror be held?
farther than the focal length
closer than the focal length
at the focal length

26. Concave Mirror F F Principal Axis
Rays traveling through focus before hitting mirror are reflected parallel to Principal Axis.
Rays traveling parallel to Principal Axis before hitting mirror are reflected through focus

27. Convex Mirror Principal Axis Focus f=-R/2
Rays are bent away from the principal axis.
Rays parallel to principal axis and near the principal axis (“paraxial rays”) all reflect so they appear to originate from the “Focus” (F).
The distance from F to the center of the mirror is called the “Focal Length” (f).

28. Concave Mirror –Drawing image
When object is on the outside of the centre of curvature
Technique
1) Parallel to principal axis reflects through f. #3
2) Through f, reflects parallel to principal axis. #2 #1
3) Through center.
4) At the vertex f V c
Image is (in this case):
Real or Imaginary
Inverted or Upright
Reduced or Enlarged
Comment that this is “weird” to have a real image. #4
**Every other ray from object tip which hits mirror will reflect through image tip. You need at least two of the above techniques to draw image

29. Concave Mirror –Drawing image
When object is on the outside of the centre of curvature
The image is real
The image is inverted
The image is smaller than the object

30. Concave Mirror-Drawing images
When object is at the centre of curvature
Technique
1) Parallel to principal axis reflects through f.
2) Through f, reflects parallel to principal axis. #1 #2
3) At the vertex f c V
Image is (in this case):
Real or Imaginary
Inverted or Upright
Reduced or Enlarged or Same Size #3
**Every other ray from object tip which hits mirror will reflect through image tip

31. Concave Mirror-Drawing images
When object is between the centre of curvature and the focus
Technique
1) Parallel to principal axis reflects through f. #2
2) Through f, reflects parallel to principal axis. #1
3) At the vertex f V c
Image is (in this case):
Real or Imaginary
Inverted or Upright
Reduced or Enlarged #3
**Every other ray from object tip which hits mirror will reflect through image tip

32. Concave Mirror Principal Rays
When object is between the focus and the Vertex
Technique
1) Parallel to principal axis reflects through f.
2) Through f, reflects parallel to principal axis. #1
3) At the vertex f V c
Image is (in this case):
Real or Imaginary
Inverted or Upright
Reduced or Enlarged #2 #3
**Every other ray from object tip which hits mirror will reflect through image tip

33. Concave Mirror Principal Rays
When object is between the focus and the Vertex
The image is virtual
The image is upright
The image is larger than the object

34. Which ray is NOT correct?
Understanding
Which ray is NOT correct?
p.a. 1) R f 2) 3)
Ray through centre should reflect back on self.

35. Mirror Focal Lengths
A concave mirror has a positive focal length f > 0
A convex mirror has a negative focal length f < 0
What is the focal length of a flat mirror?
(1) f =0 (2) f = ∞
The flatter the mirror, the larger the radius of curvature, (e.g. the earth is round, but looks flat)

36. Concave Mirror Image Location
Yep, no image

37. Mirror Equation do O f c I do = distance object is from mirror:
Positive: object is _______ of mirror
Negative: object is _______ mirror
In front
behind di
di = distance image is from mirror:
Positive: _______ image is __________ of mirror
Negative: _______ image is__________ mirror
inverted
In front
Inverted
upright
upright
behind
f = focal length mirror:
Positive: _________ mirror
Negative: _________ mirror
Concave
Convex
In Front
Behind
concave
convex

38. Understanding
The image produced by a concave mirror of a real object is:
Always Real
Always Virtual
Sometimes Real, Sometimes Virtual
Mirror Equation
In a concave mirror the focal length, f, is >0
Real Object means in front of mirror: do > 0
Therefore di can be positive or negative

39. Practice: Concave Mirror
Where in front of a concave mirror should you place an object so that the image is virtual?
Mirror Equation:
Close to mirror
Far from mirror
Either close or far
Not Possible
In a concave mirror the focal length, f, is > 0
Object in front of mirror: do > 0
Virtual image means behind mirror: di < 0
When do < f then di <0 : virtual image.

40. Magnification Equationdo O do ho
Angle of incidence
ho = height of object:
Positive:_______________ q
Always di hi
Angle of reflection I q
hi = height of image:
Positive: ______________
Negative: _____________
upright
inverted
m = magnification:
Positive / Negative: same as for hi
< 1: image is _______________
> 1: image is ________________ di
reduced q
enlarged q

41. Practice Solving Equations
A candle is placed 6 cm in front of a concave mirror with focal length f=2 cm. Determine the image location.
Real Image!
(in front of mirror)
Compared to the candle, the image will be:
Larger
Smaller
Same Size
p.a. C f
Note: image is 3 cm in front of mirror, therefore 1 cm to the left of the focus

42. Practice: Magnification
A 4 inch arrow pointing down is placed in front of a mirror that creates an image with a magnification of –2.
What is the size of the image?
2 inches
4 inches
8 inches
4 inches
Magnitude gives us size.
What direction will the image arrow point?
Up 2) Down
(-) sign tells us it’s inverted from object

43. Convex Mirror Rays Technique
1) Parallel to principal axis reflects through f.
2) Through center. #1
3) Through f, reflects parallel to principal axis. O #2 I #3 f c
Make this mirror almost flat so that it is like your rearview mirror
Image is:
Virtual (light rays don’t really cross)
Upright (same direction as object)
Reduced (smaller than object)
(always true for convex mirrors!):

44. Convex Mirror Rays The image is virtual The image is upright
The image is smaller than the object

45. Convex Mirror Images
Unlike Concave Mirrors, convex mirrors always produce images which share these characteristics. The location of the object does not affect the characteristics of the image. As such, the characteristics of the images formed by convex mirrors are easily predictable
The diagrams below shows that in each case:
the image is
located behind the convex mirror
a virtual image
an upright image
reduced in size (i.e., smaller than the object)

46. Overview Reflection: qi = qr Refraction: n1 sin(q1)= n2 sin(q2)
Last Time qi qr
qi = qr
Flat Mirror:
image equidistant behind
Spherical Mirrors:
Concave or Convex
Today q1 q2 n2 n1
Next time
Refraction:
n1 sin(q1)= n2 sin(q2)
Flat Lens:
Window
Spherical Lenses:
Concave or Convex
Absorption

47. Solving Problems Virtual Image! Image is Upright!
A candle is placed 6 cm in front of a convex mirror with focal length f=-3 cm.
Determine the image location.
Determine the magnification of the candle.
If the candle is 9 cm tall, how tall does the image candle appear to be?
di = - 2 cm (behind mirror)
Virtual Image!
Image is Upright!

48. Problem
Where should you place an object in front of a convex mirror to produce a real image?
Mirror Equation:
Object close to mirror
Object far from mirror
Either close or far
You can’t
di is negative!
f is negative
do is positive
Convex mirror: f < 0
Object in front of mirror: do > 0
Real image means di > 0

49. Problem
A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror.
At What distance from the mirror will the image be formed?
What is the height of the image? C f

50. Problem
A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror.
At What distance from the mirror will the image be formed?
What is the height of the image? C f
The image is 17 cm in front of the mirror

51. Problem
A concave mirror has a radius of curvature of 24.0 cm. An object 2.5 cm high is placed 40.0 cm in front of the mirror.
At What distance from the mirror will the image be formed?
What is the height of the image? C f
The height of the inverted image is 1.1 cm

52. Problem
A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror.
At What distance from the mirror will the image be formed?
What is the height of the image? C f

53. Problem
A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror.
At What distance from the mirror will the image be formed?
What is the height of the image? C f
Therefore the image is 0.37 m behind the mirror

54. Problem
A convex mirror has a radius of curvature of 80.0 cm. An object 1.7 m high is placed 4.5 m in front of the mirror.
At What distance from the mirror will the image be formed?
What is the height of the image? C f

55. Mirror Summary Angle of incidence = Angle of Reflection Principal Rays
Parallel to P.A.: Reflects through focus
Through focus: Reflects parallel to P.A.
Through center: Reflects back on self
|f| = R/2