TACTICS BOX $18\mathrm{.}5$ Ray tracing for a convex mirror

Draw an optical axis. Use graph paper or a ruler. Establish an appropriate scale.

Center the mirror on the axis. Mark and label the focal point at distance $f$ from the mirror's surface. Draw the mirror plane through the mirror's center, perpendicular to the axis.

Represent the object with an upright arrow at distance $s.$ It is usually best to place the base of the arrow on the axis and to draw the arrow about half the radius of the mirror.

Draw the three "special rays" from the tip of the arrow. Use a straightedge or a ruler. The rays should reflect off the mirror plane.

a$.$ A ray parallel to the axis $($Ray $1)$ reflects as though it came from the focal point.

b$.$ A ray initially directed toward the focal point $($Ray $2)$ reflects parallel to the axis.

c$.$ A ray that strikes the center of the mirror $($Ray $3)$ reflects at an equal angle on the opposite side of the optical axis.

Extend the emerging rays behind the mirror until they converge. The point of convergence is the image point. Draw the rest of the image in the image plane. If the base of the object is on the axis, then the base of the image will also be on the axis.

Measure the image distance $s^{\text{'}}.$ Also, if needed, measure the image height relative to the object height. The magnification can be found from $m=-\frac{s^{\text{'}}}{s}.$

Follow the steps above to solve the following problem: An object is $10$ cm from a convex mirror with a focal length of $9\mathrm{.}2$ cm $.$ Use ray tracing to determine the location of the image.

Part A

The diagram below shows the situation described in the problem. The focal length of the mirror is labeled $f$; the scale on the optical axis is in centimeters. Draw the three special rays Ray $1,$ Ray $2,$ and Ray $3$ as described in the Tactics Box above, and label each ray accordingly. Draw the rays from the tip of the object to the mirror plane. Do not draw the reflected rays.

Draw the vectors for the incident rays starting at the tip of the object. The location and orientation of the vectors will be graded. The length of the vector will not be graded.

$+{\displaystyle \underset{?}{\overset{?}{}}}$

Ray $1$ Ray parallel to axis

Ray $2$ Ray toward focal point

Ray $3$ Ray at mirror center