The relationship between the focal length and radius of curvature in a spherical mirror is?

Correct option is A

Ans.(a) r = 2f

Explanation:

The correct answer is r = 2f. The relationship between the focal length (f) and the radius of curvature (r) of a spherical mirror (concave or convex) is given by:

$$r=2f$$

where:

• $r$ = radius of curvature (distance from the mirror’s pole to the center of curvature)
• $f$ = focal length (distance from the mirror’s pole to the focal point)

Since the focal point is located midway between the pole and the center of curvature, we conclude that:

f=r2f = \frac{r}{2}f=r/2
​

or equivalently:

$$r=2f$$

Information Booster:

● Concave mirrors converge light, and their focal length is positive.
● Convex mirrors diverge light, and their focal length is negative.
● The focal point is the location where parallel light rays meet or appear to diverge.
● The radius of curvature is twice the focal length because the reflected rays pass through or appear to come from halfway between the mirror and its center of curvature.
● The mirror formula:

1f=1u+1v\frac{1}{f} = \frac{1}{u} + \frac{1}{v}

​1/f=1/u

​+1/v
​

relates object distance (u), image distance (v), and focal length (f).
● Applications: Used in telescopes, microscopes, car rear-view mirrors, and solar concentrators.