Chapter 23 - Physics Notes

Reflection: The change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated.
Law of Reflection: The principle that the angle of incidence is equal to the angle of reflection.
Diffuse Reflection: The phenomenon that occurs when a rough surface reflects rays so that a clear image is not visible.
Specular Reflection: The phenomenon that occurs when a smooth surface reflects light so that a clear image is visible.
Virtual Image: An image that exists only in the mind of the observer and cannot be projected on a screen.

Ray Optics

Light can be represented by a group of rays.
Light travels in reasonably straight lines.
When light strikes an object, some of the rays reflect off its surface.

Law of Reflection

The angle of incidence (θ_i) is equal to the angle of reflection (θ_r).
Both angles are measured relative to the normal line, which is perpendicular to the surface at the point of incidence.

Plane Mirrors

The brain assumes that the rays travel in straight lines, so the image appears to be located behind the mirror.
This is said to be a virtual image.
When considering a mirror image, the image we see is not actually reversed.
If two plane mirrors are set at right angles and an object is at approximately equal distances from each mirror, we see three images.
The number of images at a given angle is given by the formula n = 360° / θ - 1.
If the mirrors face each other (θ = 0°), then an infinite number of images result.

Curved Mirrors

Mirrors with curved surfaces have a variety of applications.
Concave Mirror: A mirror formed on the inside of a curved surface.
Convex Mirror: A mirror formed on the outside of a curved surface.

Concave Mirrors

To determine the location of a point on the image, we will use two specific rays from a point on the object that are reflected from the mirror’s surface.
The two rays obey the following rules:
- Incident rays that are parallel to the principal axis are reflected through the focus.
- Incident rays that pass through the focus are reflected parallel to the principal axis.
There are two additional rules:
- Incident rays that pass through the center of curvature (C) are reflected back through C.
- A ray that intersects the vertex reflects in accordance with the law of reflection from V.
There are six optically different object locations (cases) to consider.

Example: Solving a Mirror Problem

A 2.00 cm object is 12.5 cm from a concave mirror whose focal length is 5.00 cm. (a) Use ray diagrams to determine the position and height of the image. (b) Describe the image.

di = 8.3 cm

hi = –1.3 cm

The image is real, reduced, and inverted.

Magnification

Magnification is a ratio: M = hi / ho, or hi = Mho.
Positive distances are in front of the mirror.
Negative distances are behind the mirror.
Object heights are always positive; negative image heights are for inverted images.
Using the triangles in the diagram: tan θ = hi / di = ho / do
The negative sign maintains the correct sign conventions for concave and convex mirrors.
A negative magnification results in an inverted (real) image.
M = hi / ho = –di / do

Finding Image Position—Mirror Equation

The yellow triangles are similar: tan φ = hi / f = ho / (do – f)
ho / hi = (do – f) / f
do / di = do / f – 1
1 / di = 1 / f – 1 / do
1 / do + 1 / di = 1 / f

Example: Using the Mirror Equation

A 1.75 cm object is 10.0 cm from a concave mirror whose focal length is 20.0 cm. Use the mirror equation to (a) determine the position and (b) determine the height of the image. Then (c) determine the magnification of the image and (d) describe the image.

ho = 1.75 cm

f = 20.0 cm

do = 10.0 cm

di = ?

hi = ?

M = ?

1 / do + 1 / di = 1 / f

1 / 10.0 cm + 1 / di = 1 / 20.0 cm

1 / di = 1 / 20.0 cm - 1 / 10.0 cm

1 / di = 0.05 cm^–1 - 0.10 cm^–1

1 / di = -0.05 cm^–1

di = -20.0 cm

hi = -di / do × ho

hi = -(-20.0 cm) / 10.0 cm × 1.75 cm

hi = 3.50 cm

M = hi / ho

M = 3.50 cm / 1.75 cm

M = 2.00

The image is upright, enlarged, and virtual. It is 3.50 cm tall and positioned 20.0 cm behind the mirror.

Questions for Students

Define reflection and state the law of reflection.
Describe the characteristics of images formed by plane mirrors.
Explain the difference between real and virtual images formed by concave mirrors.
What type of images do convex mirrors produce?
Calculate the image position for an object placed in front of a concave mirror using the mirror equation.

Chapter 23: Light and Reflection

23.B: Reflection and Mirrors