A concave mirror is made from a portion of the surface of a sphere of radius 16.0 cm. Its principal focus will be at a distance of _______ from its pole.

Key Points

• The principal focus of a concave mirror is located at a distance equal to half the radius of curvature from its pole.
• Given the radius of curvature (R) of the concave mirror is 16.0 cm.
• The formula to find the focal length (f) of a concave mirror is f=R2f=R2 $f = \frac{R}{2}$ .
• Substituting the given value: f=16.0cm2=8.0cmf=16.0cm2=8.0cm f<mo>=<mfrac><mrow><mn>16.0<mspace><mtext>cm<mn>2<mo>=<mn>8.0<mspace><mtext>cm</mtext></mspace></mn></mo></mn></mtext></mspace></mn></mrow></mfrac></mo> $f = \frac{16.0 \, \text{cm}}{2} = 8.0 \, \text{cm}$ .
• Thus, the principal focus will be at a distance of 8.0 cm from its pole.

Additional Information

• A concave mirror, also known as a converging mirror, can form real and virtual images depending on the position of the object relative to the mirror's focus and center of curvature.
• Concave mirrors are commonly used in applications such as telescopes, shaving mirrors, and headlamps due to their ability to focus light.
• The principal axis is the line passing through the center of curvature and the pole of the mirror.
• The point where the principal axis meets the mirror surface is called the pole (P) of the mirror.
• The center of curvature (C) is the center of the sphere from which the mirror is a part, and it lies on the principal axis.