Use a ruler and a protractor to draw rays to find images in the following cases. (a) A point object located on the axis of a concave mirror located at a point within the focal length from the vertex. (b) A point object located on the axis of a concave mirror located at a point farther than the focal length from the vertex. (c) A point object located on the axis of a convex mirror located at a point within the focal length from the vertex. (d) A point object located on the axis of a convex mirror located at a point farther than the focal length from the vertex. (e) Repeat (a)-(d) for a point object off the axis.

Understanding how light interacts with mirrors is essential in the study of optics. Ray diagrams are powerful tools used to predict the location, size, and orientation of images formed by mirrors. Each ray follows the laws of reflection, and by tracing a few key rays from an object point, we can construct a visual representation of image formation.

To draw a ray diagram for mirrors, start by identifying the type of mirror (concave or convex) and its focal length. The focal length is the distance from the mirror's surface to its focal point, where parallel rays converge (concave) or appear to diverge from (convex).

For a concave mirror, there are two key rays to consider:

• A ray parallel to the principal axis will reflect through the focal point.
• A ray through the center of curvature reflects back on itself.

For a convex mirror, the reflective rays diverge, and by extending them backward, we can find their apparent point of origin.

Illustrating ray diagrams can improve comprehension and is a great way to visualize how images are formed by concave and convex mirrors, whether the object is positioned on or off the axis.

The focal length of a mirror is a key factor in determining the characteristics of the image formed. It is defined as the distance between the mirror and the focal point. In a concave mirror, the focal point is the point where parallel rays of light converging towards the mirror meet after reflection. Conversely, in a convex mirror, it is the point from which parallel rays of light appear to diverge after reflecting off the mirror.

Knowing the focal length allows us to use the mirror equation, \[ \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \.\], where \(f\) represents the focal length, \(d_o\) is the object distance, and \(d_i\) is the image distance. This equation relates these three quantities and is crucial for understanding the relation between an object and its image.

When drawing ray diagrams, the focal length helps us accurately locate the focal point and the center of curvature, providing a framework for constructing the diagram and predicting the image's nature, whether real or virtual, upright or inverted.

Reflection is a phenomenon where light 'bounces off' a surface. In mirrors, this process is governed by the law of reflection, which states that the angle of incidence (the angle at which the incoming ray approaches the mirror) is equal to the angle of reflection (the angle at which the ray departs from the mirror).

Image formation is a direct consequence of reflection. In concave mirrors, if an object is placed within the focal length, the reflected rays diverge, and the image appears behind the mirror; this is a virtual image because the light rays don't actually meet. If the object is beyond the focal length, the reflected rays converge, and the image forms in front of the mirror; this is a real image that can be projected.

Convex mirrors always produce virtual images because the parallel rays diverge upon reflection and never actually meet. Instead, they appear to come from a point behind the mirror.

It's important to remember that the location of the object in relation to the mirror's focal point is critical in determining the size, orientation, and type of image formed. This fundamental concept is at the heart of optics and is vital in real-world applications such as constructing telescopes, cameras, and designing architectural lighting.