Question

The focal length f is related to the radius of curvature r of the spherical convex mirror by:

• A. $f=r$
• B. $f=-\frac{1}{2}r$
• C. $f=+\frac{1}{2}$$r$
• D. $f=-r$

Answer 1

The correct option is C

$f=+\frac{1}{2}$$r$

Step 1: Given data:

Focal length$=F$

Center of curvature$=C$

Step 2: Formula used:

When the subject is in focus, the focal length$\left(f\right)$ of the lens is the distance between the optical center and the focus, commonly expressed in millimeters.

The radius of curvature$\left(r\right)$ is the radius of the convex or concave mirror's sphere. It's also the same as the distance between the optical center and the curvature's center.

Step 3: Calculation:

The radius of curvature for spherical mirrors with narrow apertures is found to be double the focal length. A spherical mirror's principal focus lies at the center, between the center of curvature and the optical center and the focal length of a convex lens is positive.

$$\begin{gathered} r=2f \\ f=\frac{r}{2} \end{gathered}$$

Hence, option C is the correct answer.