1. PHY 102: Lecture 9 9.1 Wave Fronts and Rays 9.2 Reflection of Light
9.3 Spherical Mirrors

2. PHY 102: Lecture 9 Reflection of Light : Mirrors
9.1 Wave Front and Rays

3. Wave Fronts and Rays - 1
Given a small spherical object whose surface is pulsating in simple harmonic motion
A sound wave is emitted that moves spherically outward from the object at a constant speed
To represent this wave, we draw surfaces through all points of the wave that are in the same phase of motion
These surfaces of constant phase are called wave fronts

4. Wave Fronts and Rays - 2
Wave fronts are concentric spherical shells about the vibrating object
If the wave fronts are drawn through the condensations, or crests, of the sound wave, the distance between adjacent wave fronts equals the wavelength 
The radial lines pointing outward from the source and perpendicular to the wave fronts are called rays

5. Wave Fronts and Rays - 3
Shows small sections of two adjacent spherical wave fronts
At large distances from the source, the wave fronts become less and less curved and approach the shape of flat surfaces

6. Wave Fronts and Rays - 4
A wave whose wave fronts are flat surfaces are plane waves

7. PHY 102: Lecture 9 Reflection of Light : Mirrors

8. Geometry of Reflection
A ray of light is incident on a flat, shiny surface
Normal is line perpendicular to surface at point of incidence
The angle of incidence qi is the angle that the incident ray makes with respect to the normal
The angle of reflection qr is the angle that the reflected ray makes with the normal

9. Law of Reflection
The incident ray, the reflected ray, and the normal to the surface all lie in the same plane
The angle of reflection equals the angle of incidence
r = i

10. Secular / Diffuse Reflection
When parallel light rays strike a smooth, plane surface, the reflected rays are parallel to each other
This type of reflection is known as specular reflection
Most surfaces are not perfectly smooth, because they contain irregularities the sizes of which are equal to or greater than the wavelength of light
The law of reflections applies to each ray, but the irregular surface reflects the light rays in various directions
This type of reflection is known as diffuse reflection

11. Formation of Images by a Plane Mirror
Properties of image in a plane (flat) mirror
Image is upright
Image is the same size
Image is located as far behind the mirror as you are in front of it
Image is same color
Image reversed right to left
Letters and words held up to a mirror are reversed

12. Illustration that Image Appears Behind Plane Mirror - 1
A light ray leaves the top of an object
This ray reflects from the mirror and enters the eye
To the eye, it appears that the ray originates from behind the mirror back along the dashed line
Actually, rays going in all direction leave each point on the object, but only a small bundle of such rays is intercepted by the eye

13. Illustration that Image Appears Behind Plane Mirror
The figure shows a bundle of two rays leaving the top of the object
All the rays that leave a given point on the object, no matter what the angle  they have when they strike the mirror, appear to originate from a corresponding point on the image behind the mirror

14. Virtual / Real Images Rays of light seem to come from the image
It is evident that they do not originate from behind the plane mirror where the image appears to be
Because none of the light rays actually emanate from the image, it is called a virtual image
Curved mirrors can produce images from which all the light rays actually do emanate
Such images are known as real images

15. Half Height Mirror
What is the minimum mirror height necessary to see full body?
Conclusion valid regardless of distance of person from mirror
To view one’s full length in a mirror, only a half-length mirror is needed
½ mirror must face upper body

16. PHY 102: Lecture 9 Reflection of Light : Mirrors
9.3 Spherical Mirrors

17. Convex / Concave Mirrors - 1
The most common type of curved mirror is a spherical mirror
A spherical mirror has the shape of a section from the surface of a sphere
If the inside surface of the mirror is polished, it is a concave mirror
If the outside surface is polished, it is a convex mirror

18. Convex / Concave Mirrors - 2
For each type mirror, the center of curvature is located at point C
Radius of curvature is R
The principal axis of the mirror is a straight line drawn through C and the midpoint of the mirror

19. Operation of Concave Mirror - 1
A point on the tree lies on the principal axis of the mirror and is beyond the center of curvature C
Light rays emanate from this point and reflect from the mirror consistent with the law of reflection
If the rays are near the principal axis, they cross it at a common point after reflection
This point is called the image point
Since light rays come from the image point, the image is real

20. Operation of Concave Mirror - 2
If tree is infinitely far away from mirror, the rays are parallel to each other and to the principal axis
Rays reflect from the mirror and pass through an image point
In this special case the image point is referred to as the focal point F of the mirror
Therefore, an object infinitely far away on the principal axis gives rise to an image at the focal point of the mirror
The distance between the focal point and the middle of the mirror is the focal length f of the mirror

21. Location of Focal Point F Concave Mirror
Focal point F lies halfway between the center of curvature C and the middle of a concave mirror
Focal length f equal one-half the radius of curvature
f = ½ R

22. When is “f = ½R” Valid
Rays that lie close to the principal axis are paraxial rays
f = ½ R is valid only for such rays
Rays that are far from the principal axis do not converge to a single point after reflection from the mirror
The result is a blurred image
The fact that a spherical mirror does not bring all rays parallel to the principal axis to a single image point is spherical aberration
Spherical aberration can be minimized by using a mirror whose height is small compared to the radius of curvature

23. Location of Focal Point F Convex Mirror
Parallel, paraxial rays are incident on a convex mirror
The rays diverge after being reflected
The reflected rays seem to come from a single point F behind the mirror
This point is the focal point of the convex mirror
Its distance from the midpoint of the mirror is the focal length f
The focal length of a convex mirror is also ½ of the radius of curvature
We assign the focal length of a convex mirror a negative value
f = -½ R

24. Formation of Images - Concave
Ray 1: Ray is initially parallel to the principal axis
Passes through the focal point F after reflecting from the mirror.
Ray 2: Ray initially passes through the focal point F
Is reflected parallel to the principal axis.
Ray 3: Ray travels along a line that passes through the center of curvature C and follows a radius of the spherical mirror
Ray strikes the mirror perpendicularly and reflects back on itself

25. Formation of Images - Concave

26. Formation of Images - Concave

27. Concave Mirror Chart Object Location Image Location Image Size
Upright Inverted
Real
Virtual
>2f (C)
>f
Small
Inverted
= 2f (C) 2f
Same
2f(C) to f
>2f
Larger
= f
Infinity -
<f
Upright

28. Convex Mirror Chart Object Location Image Location Image Size
Upright Inverted
Real
Virtual
Any where -
Smaller
Upright
Convex mirror gives wider field of view than other types of mirrors

29. Formation of Images - Convex
Ray 1: Ray is initially parallel to the principal axis
Appears to originate from the focal point F after reflection from the mirror
Ray 2: Ray heads toward F
Emerges parallel to the principal axis after reflection
Ray 3: Ray travels toward the center of curvature C
Ray strikes the mirror perpendicularly and reflects back on itself

30. Mirror Equation - Distance
do is distance of object from mirror
di is distance of image from mirror
f is focal length
- for diverging (convex) mirror
+ for converging (concave) mirror

31. Example Mirror Equation - Distance
Focal length of concave mirror is f = + 4 cm
Object is located at do = 10 cm
What is location of image, di?
(1/10) + (1/di) = +¼
(1/di) = 0.25
1/di = 0.25 – 0.10 = 0.15
di = 1/0.15 = 6.67 cm
Positive image distance means image is “real”

32. Example Mirror Equation - Distance
Focal length of convex mirror is f = - 4 cm
Object is located at do = 10 cm
What is location of image, di?
(1/10) + (1/di) = -¼
(1/di) = -0.25
1/di = – 0.10 = -0.35
di = -1/0.35 = cm
Negative image distance means image is “virtual”

33. Mirror Equation – Size or Magnification
Positive magnification means upright image
Negative magnification means inverted image

34. Example Magnification Equation
Focal length of concave lens is f = + 4 cm
Object is located at do = 10 cm
Image is located at di = 6.67 cm
Magnification = / 10 =
The image is inverted and smaller

35. Example Magnification Equation
Focal length of convex lens is f = - 4 cm
Object is located at do = 10 cm
Image is located at di = cm
Magnification = - (-2.87) / 10 =
The image is upright and smaller