1. Reflection and Refraction
Chapter 26
Reflection and Refraction

2. A Brief History of Light
1000 AD
It was proposed that light consisted of tiny particles
Newton
Used this particle model to explain reflection and refraction
Huygens
1670
Explained many properties of light by proposing light was wave-like

3. A Brief History of Light, cont
Young
1801
Strong support for wave theory by showing interference
Maxwell
1865
Electromagnetic waves travel at the speed of light

4. A Brief History of Light, final
Planck
EM radiation is quantized
Implies particles
Explained light spectrum emitted by hot objects
Einstein
Particle nature of light
Explained the photoelectric effect

5. Geometric Optics – Using a Ray Approximation
Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media
The ray approximation is used to represent beams of light
A ray of light is an imaginary line drawn along the direction of travel of the light beams

6. Ray Approximation
A wave front is a surface passing through points of a wave that have the same phase and amplitude
The rays, corresponding to the direction of the wave motion, are perpendicular to the wave fronts

7. Reflection of Light
A ray of light, the incident ray, travels in a medium
When it encounters a boundary with a second medium, part of the incident ray is reflected back into the first medium
This means it is directed backward into the first medium

8. Specular Reflection
Specular reflection is reflection from a smooth surface
The reflected rays are parallel to each other
All reflection in this text is assumed to be specular

9. Diffuse Reflection
Diffuse reflection is reflection from a rough surface
The reflected rays travel in a variety of directions
Diffuse reflection makes the road easy to see at night

10. Law of Reflection The normal is a line perpendicular to the surface
It is at the point where the incident ray strikes the surface
The incident ray makes an angle of θ1 with the normal
The reflected ray makes an angle of θ1’ with the normal

11. Law of Reflection, cont
The angle of reflection is equal to the angle of incidence
θ1= θ1’

12. Image forms at the point where the light rays converge.
When we talk about an image, start from an ideal point light source.
Every object can be constructed as a collection of point light sources.
VIRTUAL
IMAGE
|q| p
Image forms at the point where the light rays converge.
When real light rays converge  Real Image
When imaginary extension of L.R. converge  Virtual Image
Only real image can be viewed on screen placed at the spot.

13. For plane mirror: p = |q|
IMAGE
VIRTUAL
For plane mirror: p = |q|
How about left-right? Let’s check?

14. Parallel light rays: your point light source is very far away.
Spherical Mirror
R: radius of curvature
focal Point
f: focal length = R/2
Optical axis
concave
convex
Parallel light rays: your point light source is very far away.
Focal point:
(i) Parallel incident rays converge after reflection
(ii) image of a far away point light source forms
(iii) On the optical axis

15. Spherical Aberration Reflected rays do not converge:
Not well-defined focal point
not clear image
Spherical Aberration
f = R/2 holds strictly for a very
narrow beam.
Parabolic mirror can fix this problem.

16. Spherical Aberration:
some mirrors were ground wrong by
1/50th of human hair thickness.

18. Notation for Mirrors
The object distance is the distance from the object to the mirror
Denoted by p
The image distance is the distance from the image to the mirror
Denoted by q
The lateral magnification of the mirror is the ratio of the image height to the object height
Denoted by M

19. Types of Images for Mirrors
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

20. 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

21. Flat Mirror Simplest possible mirror
Properties of the image can be determined by geometry
One ray starts at P, follows path PQ and reflects back on itself
A second ray follows path PR and reflects according to the Law of Reflection

22. Properties of the Image Formed by a Flat Mirror
The image is as far behind the mirror as the object is in front
|q| = p
The image is unmagnified
The image height is the same as the object height
h’ = h and M = 1
The image is virtual
The image is upright
It has the same orientation as the object
There is an apparent left-right reversal in the image

23. Case 1: p > R p f q
P > q
Real Image

24. Case 2: p = R
p = q
Real Image

25. Case 3: f < p < R
p < q
Real Image

26. Case 4: p = f
q = infinite

27. Case 5: p < f
q < 0
Virtual Image

28. For a small object, f = R/2 (spherical mirror)
Mirror Equation
1/p + 1/q = 1/f
For a small object, f = R/2 (spherical mirror)
1/p + 1/q = 2/R
Alert!!
Be careful with the sign!!
Negative means that it is inside the mirror!!
p can never be negative (why?)
negative q means the image is formed inside the mirror
VIRTUAL
How about f?

29. Focal point inside the mirror
For a concave mirror: f > 0
Focal point inside the mirror
f < 0
1/p + 1/q = 1/f < 0 : q should be negative.

30. All images formed by a convex mirror are VIRTUAL.
1/p + 1/q = 1/f < 0 : q should be negative.
All images formed by a convex mirror are VIRTUAL.
Magnification, M = -q/p
Negative M means that the image is upside-down.
For real images, q > 0 and M < 0 (upside-down).

31. Sign Conventions for Mirrors
Quantity
Positive When
Negative When
Object location (p)
Object is in front of the mirror
Object is behind the mirror
Image location (q)
Image is in front of mirror
Image is behind mirror
Image height (h’)
Image is upright
Image is inverted
Focal length (f) and radius (R)
Mirror is concave
Mirror is convex
Magnification (M)

32. Ex. 26.1 An object is placed at the center of curvature of a
Mirror. Where is the image formed? Describe the image?
1/p + 1/q = 1/f f = R/2
Object is at the center: p = R
1/q = 1/f – 1/p
= 2/R – 1/R
= 1/R
q = R > 0 (Real Image)
M = -q/p = -R/R = -1
No magnification but upside-down

33. Up-right or Upside-down
Ex A concave mirror has a 30 cm radius of curvature.
If an object is placed 10 cm from the mirror, where will the
image be found?
f = R/2 = 15 cm, p = 10 cm
1/p + 1/q = 1/f  1/10 + 1/q = 1/15
3/30 + 1/q = 2/30
1/q = -1/30
q = -30 cm
Case 5: p < f
Real or Virtual
Magnified or Reduced
Up-right or Upside-down
q < 0
M = -q/p = 3

34. Q. An upright image that is one-half as large as an object is
needed to be formed on a screen in a laboratory experiment
using only a concave mirror with 1 m radius of curvature.
If you can make this image, I will give you $10. If you can’t
you should pay me $10. Deal or no deal? Why?
1/p + 1/q = 1/f = 2/R > 0
M = -q/p = ½ > 0
should be a real image: q > 0
M = -q/p cannot be positive, if q > 0.
No deal!!!