For a spherical concave mirror in the paraxial approximation, which statement correctly relates the focal length $f$ to the radius of curvature $R$?

An object is placed $24$ cm in front of a concave mirror with focal length $8$ cm. What is the image distance?

A concave mirror with focal length $15$ cm forms an image $60$ cm in front of the mirror. What object distance and image description are consistent with this situation?

Which set of image properties is always produced by a convex mirror for a real object?

An object is placed $18$ cm in front of a convex mirror of focal length $9.0$ cm in magnitude. Using the standard sign convention, what is the image distance?

For a convex mirror with $f=-10$ cm and an object at $d_o=15$ cm, which proposed solution is physically consistent?

What best explains why a lens changes the direction of light rays while a mirror changes them differently?

A diverging lens has a focal length of $-20$ $\text{cm}$, and an object is placed $30$ $\text{cm}$ in front of it. What is the image distance?

You are designing a quick sketch procedure for a lab manual. Which pair of rays is guaranteed to be sufficient for locating the image in a thin-lens ray diagram when drawn correctly?