TACTICS BOX $18\mathrm{.}4$ Ray tracing for a concave mirror

Draw an optical axis. Use graph paper and 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. The rays should reflect of the mirror plane.

a$.$ A ray parallel to the axis $($Ray $1)$ reflects through the focal point.

b$.$ An incoming ray that passes through the focal point $($Ray $2)$ reflects back 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 rays until they converge. The rays converge at 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 problem: An object is $18\mathrm{.}0$ cm from a concave mirror with a focal length of $7\mathrm{.}5$ 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 $($dashed vertical line$).$ Do not draw the reflected rays.

Draw the vectors starting from the tip of the object making use of the crosshair to locate the tip. The location and orientation of the vectors will be graded.

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