1. Geometrical Optics (Lecture II)
Chapter 26
Geometrical Optics (Lecture II)
Dr. Jie Zou
PHY 1161

2. Outline Forming images with a plane mirror Spherical mirrors
Real world application: retroreflector
Spherical mirrors
Concave mirror and convex mirror
Forming images with a concave or convex mirror
Ray tracing (ray diagram)
Mirror equation
Dr. Jie Zou
PHY 1161

3. Forming Images with a Plane Mirror
Forming a mirror image:
The light from an object reflects from a mirror before it enters our eyes.
To the observer, it appears that the rays are emanating from behind the mirror.
Some properties of a plane mirror image:
It is upright, but appears reversed right to left.
It is the same distance behind the mirror as the object is in front of the mirror.
It is the same size as the object.
It is a virtual but NOT a real image.
Dr. Jie Zou
PHY 1161

4. Real World Applications
Retroreflection: If the angle between the two mirrors is 90°, the reflected beam will return to the source parallel to its original path.
Dr. Jie Zou
PHY 1161

5. Spherical Mirrors
A spherical mirror has the same shape as a section of a sphere.
Concave mirror: The inside surface is reflecting.
Convex mirror: The outside surface is a reflecting.
Center of curvature C: the center of the sphere with radius R of which the mirror is a section.
Principal axis: a straight line drawn through the center of curvature and the midpoint of the mirror.
Focal point and focal length (see next slide)
Dr. Jie Zou
PHY 1161

6. Focal Point and Focal Length of Convex and Concave Mirrors
Focal point F
Focal length f:
For a convex mirror: f = - (1/2)R. “-” sign indicates that the focal point F lies behind the mirror.
For a concave mirror: f = (1/2)R. “+” sign indicates that the focal point is in front of the mirror. In this case, the rays of light actually pass through and converge at the focal point F.
Convex mirror
Dr. Jie Zou
PHY 1161
Concave mirror

7. Forming Images with a Convex and Concave Mirror
Two techniques to find the orientation, size, and location of an image formed by a spherical mirror:
(1) Ray tracing (ray diagram): Gives the orientation of the image as well as qualitative information on its location and size.
(2) Mirror equation: Provides precise and quantitative information without the need for accurate scale drawing.
Dr. Jie Zou
PHY 1161

8. Raying Tracing Basic idea behind ray tracing:
Follow the path of representative rays of light as they reflect from a mirror and form an image.
Three representative rays:
(1) Parallel ray (P ray): a ray parallel to the principle axis of the mirror
(2) Focal-point ray (F ray): a ray that passes through (concave mirror) or moves toward (convex mirror) the focal point F
(3) Center-of-curvature ray (C ray): a ray that moves along a straight line extending from the center of curvature C
Concave mirror
Dr. Jie Zou
PHY 1161
Convex mirror

9. Ray Diagram for a Convex Mirror
Image properties:
It is a virtual image: no light actually passes through the image.
Orientation: upright (the same orientation as the object).
Size: smaller than the object.
Location: between the mirror and the focal point F.
Dr. Jie Zou
PHY 1161

10. Ray Diagram for a Concave Mirror
Consider three situations, (a), (b) and (c)
Question: Is a makeup mirror concave or convex?
(b)
Dr. Jie Zou
PHY 1161

11. Mirror Equation Mirror equation: Magnification, m: m = hi/ho= - di/do
(1/do) + (1/di) = 1/f
do (object distance): distance from the mirror to the object.
di (image distance): distance from the mirror to the image.
f: the focal length of the spherical mirror.
Magnification, m: m = hi/ho= - di/do
hi: height of the image
ho: height of the object
Dr. Jie Zou
PHY 1161

12. Sign Conventions for the Mirror Equation
Focal length
f >0 for concave mirrors
f<0 for convex mirrors
Magnification
m>0 for upright images
m<0 for inverted images
Image distance
di >0 for images in front of a mirror (real images)
di<0 for images behind a mirror (virtual images)
Object distance
do>0 for objects in front of a mirror (real objects)
do<0 for objects behind a mirror (virtual objects)
Dr. Jie Zou
PHY 1161

13. Examples
Exercise 26-1: The concave side of a spoon has a focal length of 5.00 cm. Find the image distance for this “mirror” when the object distance is (a) 25.0 cm, (b) 9.00 cm, and (c) 2.00 cm. Also, is the image in each case real or virtual? Upright or inverted? Smaller or enlarged?
Exercise 26-2: The convex mirror has a 20.0-cm radius of curvature. Find the image distance for this mirror when the object distance is 6.33 cm.
Dr. Jie Zou
PHY 1161

14. Homework #12
Chapter 26, P , Problems: #1, 10, 18, 28, 29, 31 (Physics, Walker, 4th edition).
Dr. Jie Zou
PHY 1161