Final answer:
A dentist uses a concave mirror to magnify teeth, which reflects light inward and enlarges close objects. The warning on car mirrors 'Objects in the mirror are closer than they appear' refers to convex mirrors, which make objects appear smaller and further away than they actually are. One can determine a mirror's shape by observing the characteristics of the reflected images.
Step-by-step explanation:
The type of mirror a dentist uses to magnify teeth is a concave mirror. Concave mirrors can create magnified images when the object is placed close to the mirror. Since dentists require a larger view of a patient's teeth to better see details and work accurately, the concave mirror is ideal because it reflects light inward to a focal point, hence magnifying objects that are close to it.
On the other hand, the statement "Objects in the mirror are closer than they appear" is commonly found on convex mirrors, like those on the driver's side of a car. Convex mirrors have a diverging effect on light rays, making objects appear smaller and further away. This is why the warning statement is necessary: to remind the driver that objects reflected in the convex side mirror are actually closer than the reduced image suggests.
To experimentally confirm the shape of a mirror, one could observe the way light is reflected. If the reflection causes objects to appear larger and is capable of projecting an image onto a surface when the object is close, the mirror is concave. If the reflection causes objects to look smaller and further away, and the reflected image appears behind the actual mirror and is not projectable, it indicates a convex mirror.