Final answer:
The mirror in question is a concave mirror with a focal length of 45 cm, inferred from the given magnification and the distance between the object and the image.
Step-by-step explanation:
To determine what kind of spherical mirror is used (concave or convex) and its focal length when a small candle is placed on its optical axis with a magnification of 2.00 and the distance between object and image is 45.0 cm, we can use the mirror equation and the magnification formula.
The mirror equation is 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance. The magnification m is given by -di/do for mirrors, and a positive magnification indicates a virtual image while a negative magnification indicates a real image.
Given a magnification of 2, this implies that the image is virtual and upright, hence the mirror is concave. From the magnification m = -di/do = 2, we know that di = -2do. Since the distance between the object and image is 45 cm (do + di = 45 cm), we can solve for do and di.
Substituting di = -2do into do + di = 45 cm, we get to do - 2do = -45 cm or do = 45 cm, and hence di = -90 cm. We can now use these values in the mirror equation to calculate the focal length:
1/f = 1/do + 1/di = 1/45 - 1/90 = 1/90 cm-1, so the focal length f = 90 cm / 2 = 45 cm.
Therefore, the focal length of the mirror is 45 cm, and because the image is virtual and enlarged, the mirror is concave.