Question

ray tracing for a concave mirror
an object o is placed at the location shown in front of a concave spherical mirror. use ray tracing to determine the location and size of the reflected image. as you work, keep in mind the following properties of principal rays

1. a ray parallel to the axis, after reflection, passes through the focal point f of a concave mirror or appears to come from the (virtual) focal point of a convex mirror
2. a ray through (or proceeding toward) the focal point f is reflected parallel to the axis
3. a ray along the radius through or away from the center of curvature c intersects the surface normally and is reflected back along its original path
4. a ray to the vertex v is reflected, forming equal angles with the optic axis

now trace the path of a ray emitted from the tip of the object parallel to the axis of the mirror and then the reflected ray that results. start by extending the existing incident ray emitted from the tip of the object until it reaches the mirror. then create the reflected ray starting from the point where the incident ray hits the mirror.
for the incident ray, the end point will be graded. for the reflected ray, the start point and orientation will be graded.

Explanation:

Step1: Extend the Incident Ray

The incident ray from the tip of object \( O \) is parallel to the optic axis. Extend this ray (the purple arrow) until it hits the concave mirror surface (at point \( V \) or the mirror's edge, depending on the diagram; here, follow the horizontal path to the mirror).

Step2: Draw the Reflected Ray

For a concave mirror, a ray parallel to the axis reflects through the focal point \( F \). So, from the point where the incident ray hits the mirror, draw a ray towards \( F \) (or through \( F \), depending on the mirror's position). The start point is the mirror - incident point, and the orientation is towards \( F \) (or through \( F \) for real reflection in concave mirror case here).

Answer:

1. Extend the horizontal (parallel to axis) incident ray from \( O \) until it intersects the concave mirror.
2. Draw the reflected ray starting from the mirror - intersection point, passing through the focal point \( F \) (for concave mirror, parallel - axis incident ray reflects through \( F \)).