Final answer:
The magnitude of the focal length of a spherical convex mirror with radius of curvature R is R/2. The correct option is E.
Step-by-step explanation:
If a spherical convex mirror has a radius of curvature R, the magnitude of its focal length is E. R/2.
Using the principles of optics, specifically the law of reflection and some basic trigonometry in the context of mirrors, we discern that for any spherical mirror, the focal length (f) is half the radius of curvature (R).
This conclusion, which holds true when dealing with the small-angle approximation, is framed by the relationship R = 2f. Accordingly, this tells us that f = R/2, which implies that the focal point lies midway along the radius of curvature.
Even without relying heavily on simplifications, this relationship between the focal length and the radius of curvature is fundamental in mirror optics. For a convex mirror, the focal length is considered negative; however, when discussing magnitudes, we take the absolute value, making the focal length for a convex mirror with radius of curvature R to be R/2.