Question

What is the relation between the focal length (f) and radius of curvature (R) of spherical mirrors?

• A. R = 2f
• B. R = 3f
• C. f = 2R
• D. f = 3R

Answer 1

Answer:

A. R = 2f

• The focal length (f) of a spherical mirror is exactly half of its radius of curvature (R).

• The formula is expressed as: f = R / 2 or R = 2f.

• Radius of Curvature (R): This is the radius of the hollow sphere of glass from which the mirror is cut.

• It is the distance between the center of curvature (C) and the pole (P) of the mirror.

• Focal Length (f): This is the distance between the principal focus (F) and the pole (P) of the mirror.

• Paraxial Rays: This relationship is valid only for spherical mirrors where the aperture is small compared to the radius of curvature.

• Rays that are incident close to the principal axis are called paraxial rays, and they converge at or appear to diverge from the principal focus.

• Sign Convention: In the Cartesian sign convention used for mirrors:

  • For a Concave Mirror: The focus and center of curvature lie in front of the mirror, so both f and R are negative.

  • For a Convex Mirror: The focus and center of curvature lie behind the mirror, so both f and R are positive.