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Image Formation on Concave Mirrors

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Image Formation on Concave Mirrors


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Students explore the physics behind concave mirrors.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • After completing this Activity Object, students will be able to:
  • Predict image formation on concave mirrors.
  • Show special rays on concave mirrors.
  • Perform experiments for different locations of an object on concave mirrors.
  • Draw the formation of an image on concave mirrors.
  • Calculate the location and height of an image on concave mirrors.

Everything You'll Have Covered

Because light travels in a straight line, we can observe the properties of mirrors. Mirrors reflect light. Incident light is what "bounces" off the mirror and becomes reflected light. The mirror is the surface where the reflection of the light occurs. Reflected light forms an image. If we use a few special light rays, we can follow the light that passes from the object to the mirror and then reflects to create an image. Where these special rays intersect, an image is formed.

A spherical concave mirror is a section of a sphere that reflects light off the inner concave surface. Since many concave mirrors are spherical, they have a radius of curvature R (see diagram below), which is the distance from the center of the sphere to the reflective surface. The center of the sphere is known as the center of curvature, denoted by C in the diagram. The exact midpoint of the concave section is known as the vertex (V) of the mirror. The line that runs through Points V and C is the principal axis (red line). Incident light rays that are parallel to the principal axis are all reflected through the focal point F. The focal length (f) is the distance from the surface of the mirror to the focal point and is one-half the radius of the curvature, f = R/2.

Any incident light ray that passes through the center of curvature (C) is reflected directly back on itself. Any incident ray on the vertex at a given angle to one side of the principal axis will be reflected at the same angle on the opposite side of the principal axis.

The light rays from an object are reflected off the mirror. An image is then formed where the reflected light rays intersect. Reflected light rays may intersect on either side of the mirror. An image that is formed when reflected rays appear to intersect behind the mirror is called a virtual image. Conversely, when light rays actually intersect in front of the mirror, the image is a real image. Real images can be projected onto a screen, while virtual images cannot. Depending on where the object is located with respect to Points V, F, and C, the images formed may be real or virtual, inverted, and the size of the image may change.

  • If the object is located farther away than Point C, the image is real, inverted, and smaller than the object.
  • If the object is located at Point C, the image is real, inverted, and equal in size to the object.
  • If the object is located between Points C and F, the image is real, inverted, and magnified.
  • If the object is located between Points F and V, the image is virtual, right-side up, and magnified.

You can find the object's distance from the mirror, and the image's distance from the mirror using the mirror equation: where f is the focal length. These distances, as well as the height of the object and the height of the image can give us the magnification: If the image is inverted, is negative. If the image is virtual, is negative.

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Students explore the physics behind concave mirrors.
Course Physics
Type of Tutorial Concept Development
Key Vocabulary center of curvature, concave mirrors, converging mirrors