http://www.ck12.org Chapter 20. Geometric Optics
Check Your Understanding
If an object is placed at the focal point of a concave mirror, where does the image form?
Answer:Using the mirror equation anddo=f:
1
do+
1
di=
1
f→
1
f+
1
di=
1
f
1
di= 0
di→∞The image would form at "infinity.” No image is formed since the rays would never converge. They reflect off the
mirror parallel to the principal axis. This is why your image would vanish in going from inverted to upright as stated
above.
Convex Mirrors
A convex mirror is shown inFigure20.13.
Convex mirrors give wide views. They reduce the object size, and therefore can fit large views into small areas.
Convex mirrors are often placed in stores above customer’s heads, and are also used as side-view mirrors in cars.
Constructing ray diagrams for convex mirrors
Three principal rays can be drawn to construct ray diagrams for convex mirrors.
Ray 1: A ray that would pass through the focal point is reflected parallel to the principal axis.
Ray 2: A ray that is parallel to the principal axis reflects as if in line with the focal point.
Ray 3: A ray that would pass through the center of curvature is reflected back upon itself.
Sign Conventions for convex mirrors.
- Distances are all measured from the mirror.
- The focal length of a convex mirror is assumed to be negative.
- The image distance is always negative.
- The object and the image heights are always positive.
- The magnification (always less than 1) is given by the same equation as for a concave mirror.
Concluding remarks for convex mirrors
An object placed anywhere (farther or closer than the focal point) in front of a convex mirror always produces a
reduced, upright, and virtual image.
Illustrative Example 21.2.2
An object of height 10.0 cm object is placed 20.0 cm from a convex mirror of focal length -12.0 cm.