11.9- Images in Curved Mirrors -Concave

         11.9: Images in Concave Curved Mirror

What is a Concave Mirror?

A concave mirror or converging mirrors, has a reflecting surface that bulges inward (away from the incident light). Concave mirrors reflect light inward to one focal point. They are used to focus light. Unlike convex mirrors, concave mirrors show different image types depending on the distance between the object and the mirror.

These mirrors are called "converging mirrors" because they tend to collect light that falls on them, refocusing parallel incoming rays toward a focus. This is because the light is reflected at different angles, since the normal to the surface differs with each spot on the mirror.                          

Uses of Concave Mirrors

Concave mirrors are used in reflecting telescopes. They are also used to provide a magnified image of the face for applying make-up or shaving. In illumination applications, concave mirrors are used to gather light from a small source and direct it outward in a beam as in torches, headlamps and spotlights, or to collect light from a large area and focus it into a small spot. Concave mirrors are used to form optical cavities, which are important in laser construction.

Key Terms for Concave Mirrors

The following are terms that you must know:
Principle Axis - The line that passes through the centre of curvature. It is also normal to the centre of the mirror. 

Centre of Curvature (C) - The point where all normals meet.

Vertex (V) - The point where the principal axis cuts the centre of the mirror. 

Focal Point (F) - When incident rays are near and parallel to the principal axis, their reflected rays all pass through the same point on the principal axis.  This point is called the focal point.  

Focal Length (f) - This is the distance between the vertex and the focal point.

 
Radius of Curvature (R) - This is the distance from the vertex to the centre of curvature

 

The point on the mirror's surface where the principal axis meets the mirror is known as the vertex and is represented by the letter A in the diagram below. The vertex is known as the geometric center of the mirror. The point between the vertex and the center of curvature is known as the focal point. The focal point is represented by the letter F in the diagram below. The distance from the vertex to the center of curvature is known as the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut. Finally, the distance from the mirror to the focal point is known as the focal length (represented by f). The focal length would be one-half the radius of curvature, since the focal point is the midpoint of the line segment adjoining the vertex and the center of curvature.

Principal axis	Center of Curvature	Vertex
Focal Point	Radius of Curvature	Focal Length

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Concave Mirrors Ray Diagram

A concave mirror diagram showing the focus, centre of curvature, and the principal axis.

Object's position	Image
(Object between focal point and mirror)	Virtual Upright Magnified (larger)
(Object at focal point)	Reflected rays are parallel and never meet, so no image is formed. In the limit where S approaches F, the image distance approaches infinity, and the image can be either real or virtual and either upright or inverted depending on whether S approaches F from above or below.
(Object between focus and centre of curvature)	Real image Inverted (vertically) Magnified (larger)
(Object at centre of curvature)	Real image Inverted (vertically) Same size Image formed at centre of curvature
(Object beyond centre of curvature)	Real image Inverted (vertically) Reduced (diminished/smaller) As the distance of the object increases, the image approaches the focal point In the limit where S approaches infinity, the image size approaches zero as the image approaches F