1. Concave Mirrors
A concave spherical mirror a mirror whose reflecting surface is a segment of the inside of a sphere.
Concave mirrors are used to magnify objects.
The radius of curvature, R, determines where the image will appear in the mirror and how large the image will be. It is the same radius as the spherical shell, therefore R is the distance from the mirror’s surface to the center of curvature, C.

2. Concave Mirrors
The line passing through the center of the sphere and attaching to the mirror in the exact center of the mirror is the principal axis.
The point in the center of the sphere from which the mirror was sliced is known as the center of curvature and is denoted by the letter C . Sometimes a figure of 2F is used at this point.
The point on the mirror's surface where the principal axis meets the mirror is known as the vertex - V. The vertex is the geometric center of the mirror.
Midway between the vertex and the center of curvature is a point known as the focal point or principal focus ; the focal point is denoted by the letter F.

3. Concave Mirrors

4. Concave Mirrors
With a concave mirror, light rays diverge from an object and reflect off the mirror. They converge at a distance, q, which is in front of the mirror. Because the light rays reflected by the mirror actually pass through the image point, the image forms in front of the mirror.

5. Concave Mirrors

6. Concave Mirrors Images formed from concave mirrors are real images.
Real image = an image that is formed by the intersection of light rays; a real image can be projected on a screen.
Focal point = a point on the principal axis where the light rays pass through to form an image.
Focal length = the distance from the focal point to the mirror.

7. 1/object distance + 1/image distance = 1/focal length
Concave Mirrors
The Mirror Equation:
1/p + 1/q = 2/R
1/object distance + 1/image distance = 1/focal length
R = 2f
1/p + 1/q = 1/f
Distances are positive when measured in front of the mirror and negative when behind the mirror.

8. Concave Mirrors
Magnification = a measure of how large or small the image is with respect to the original size.
M = h’/h = -q/p
Magnification = image height/object height
Magnification = -(image distance)/(object distance)
If the image is smaller than the object, the magnification is less than 1.
If the image is larger than the object, the magnification is greater than 1.
If M is negative, the image is upside down.

9. Concave Mirrors
Ex: A concave mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image. G: f = 10.0 cm S: 1/q = 1/10.0 – 1/30.0 p = 30.0 cm S: q = 15.0 cm U: q E: 1/p + 1/q = 1/f M = -q/p 1/q = 1/f – 1/p M = -15.0/30.0 = -0.50