# Concave Mirrors

## Reflection from a Concave Spherical Mirror

Figure 2. Reflection from a concave spherical mirror.

If the light is reflected from a curve mirror what happens dependends on where the object is on the axis. The point C is the centre of curvature of the mirror. The point F is the focus of the mirror. This is the point at which the rays of light parallel to the axis converge after being reflected.

Flash Animation: a concave circular section mirror

The flash animation shows a curved mirror with a circular curvature of radius 300 mm. As object placed at the center of the mirror can be moved along the optical axis. The resulting image from the mirror is also shown. When the mouse button is pressed two rays are drawn. One ray is parallel with the optical axis to the mirror, this ray is reflected through the focus F. A second ray from the top of the oject passes through the focus, F and is reflected along the optical axis. Where the two rays coincide the image will be formed. The height and orientation of the image depends on the position of the object in relation to the center of curvature and focus.The magnification factor is given by the height of the image divided by the height of the image.

### Object Beyond C

Figure 3. Reflection from a concave mirror.

For an object positioined beyond the center of curvature, C, the resulting image will be inverted and reduced. When the object is placed at the centre of curvature, the image will be the same height as the object but will still be inverted.

### Object Between C and F

Figure 4. Reflection from a concave mirror.

When the object is positioned in between C and F the image is inverted and appears smaller than the object. The magnification factor is less than 1.

Figure 5. Reflection from a concave mirror.

As the object moves toward the focal point F the image size increase and until at F the image is infinite in height.

### Object Beyond F

Beyond F the image becomes virtual that is it cannot be projected. The image is also no longer inverted but is magnified. As the object moves closer to the mirror's surface the magnification of the virtual image decreases.

## Wide Apperture Mirrors

We have talked about mirrors with a circular curvature as converging a single point but this is only true if the radius of curvature C is large compared to the aperture of the mirror.

If the aperture of the mirror is close to the size of the radius of curvature then the rays converge at different points with distance from the optical axis. The line of point produced by each set of rays is known as a caustic curve