Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
A spherical mirror is a mirror whose reflecting surface is a part of a hollow sphere of glass.
A Concave Mirror has a reflecting surface that is curved inwards (towards the center of the sphere). It is called a converging mirror because light rays parallel to the principal axis converge at a single point after reflection.
A Convex Mirror has a reflecting surface that is curved outwards. It is called a diverging mirror because light rays parallel to the principal axis appear to diverge from a point behind the mirror after reflection.
The Pole () is the geometric center of the reflecting surface of the spherical mirror.
The Center of Curvature () is the center of the hollow sphere of which the mirror is a part.
The Radius of Curvature () is the distance between the Pole and the Center of Curvature ().
The Principal Axis is an imaginary straight line passing through the Pole () and the Center of Curvature () of the mirror.
The Principal Focus () is a point on the principal axis where rays of light parallel to the axis actually meet (in a concave mirror) or appear to diverge from (in a convex mirror) after reflection.
The Focal Length () is the distance between the Pole () and the Principal Focus () of the mirror.
For spherical mirrors of small apertures, the radius of curvature is found to be twice the focal length, expressed as .
📐Formulae
💡Examples
Problem 1:
If the radius of curvature of a concave mirror is , what is its focal length?
Solution:
Explanation:
The focal length of a spherical mirror is exactly half of its radius of curvature. Given , we divide by to find .
Problem 2:
A convex mirror has a focal length of . Calculate its radius of curvature.
Solution:
Explanation:
The radius of curvature is twice the focal length. Since , we multiply by to find .
Problem 3:
An object is placed at the Center of Curvature of a concave mirror. If the distance of the Center of Curvature from the Pole is , find the distance of the Focus from the Pole.
Solution:
Explanation:
The distance of the Center of Curvature from the Pole is the Radius of Curvature (). The distance of the Focus from the Pole is the Focal Length (). Using , we get .