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We see an object because light from the object travels into our eyes. Sometimes light from the object reflects off a mirror or has been refracted by an object and travels to our eyes by other than a straight path. When this happens the brain tells us that the image is where the rays that enter the eye appear to have come from. In other words the eye 'traces the rays back' to the source (or where it appears to be)! |
| Concave mirrors can be thought of as being made from the silvered inside of a sphere. If we took a sphere that was silvered on the inside and chopped off a section of it we would have a concave mirror. |
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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. The following facts are used to construc ray diagrams: |
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The distance from the vertex to the centre of curvature is called the radius of curvature (represented by R). The radius of curvature is the radius of the sphere from which the mirror was cut. |
| The distance from the vertex to the focal point is known as the focal length - f. As the focal point is the midpoint of the line joining the vertex and the center of curvature, the focal length is one-half the radius of curvature. |
We can use the following three facts to construct ray diagrams for curved mirrors:
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Any ray travelling parallel to the principal axis on its way to the mirror will pass through the focal point upon reflection.
Because the sun is such a large distance from the Earth, all light rays from the sun are travelling parallel to each other. If you make them travel along the principal axis they will be brought to a sharp focus. A concave mirror can therefore easily set alight objects such as curtains that happen to be at the focal point when the sun is shining onto the mirror. Therefore you usually see a warning sticker on such mirrors when you purchase them.
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Any ray passing through the focal point on the way to the mirror will travel parallel to the princpal axis upon reflection.
Curved reflectors are used to make parallel rays of energy emerge from them. For example a curved reflector is used to give off parallel rays of infra red energy from the heating element of an electric fire. the heating element is placed at the focus and the rays that are reflected by the back of the fire come out in a parallel beam.
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Any ray that passes through the centre of curvature of the mirror will reflect back along its own path because the radius of a circle always hits the edge of the circle at 90 degrees - it hits it normally so the angle of incidence and reflection will both be zero. |
To construct a ray diagram for a concave mirror
- Draw the principal axis across your page.
- Using a compass draw the curved mirror so that it is bisected at the principlal axis. Ray diagrams are drawn to scale - so whatever value you are given for the focal length of the mirror will be doubled for the radius of the circle that you draw for the mirror.
- Add the chevron shading.
- Label the point that your compass went through C (or 2F) and the point where the line of the principal axis cuts the mirror V.
- Measure CV and put a point F halfway along the principal axis.
- Place your object point (to scale) on your diagram. Add an arrow going from the principal axis to that point (pointing towards it!).
- Take a ray from the object through 2F (or C) to the mirror. Add two arrow heads on it in opposite directions.
- Take a ray from the object point travelling parallel to the principal axis and mak it hit the mirror. (Add the arrow). Now make it reflect so that it passes through F. (Add the arrow)
- Take a ray from the object and make it pass through F on its way to the mirror. (Add the arrow). Make it reflect from the mirror so that it travels parallel to the principal axis.
If you have drawn your diagram carefully the rays will all cross at one point. That is your image point. Label it and then draw an arrow going from the principal axis to that point.
1. Object beyond C
2. Object between C and F
3. Object between V and F
4. Object At F
5. Object At C
Is the image formed upright or inverted?
Ray diagrams of concave lenses are constructed from the principal axis line - the object is a point (shown by an arrow, the base of which starts at the principal axis) - the image point when found is then also highlighted by an arrow that originates on the principal axis - that shows you which way up the image is.
Is the image formed real or virtual?
If the image is formed at the junction of rays it is real. If it is formed at the junction of construction lines - drawn out from diverging rays - it is virtual and should be drawn as a dashed arrow..
Uses of concave mirrors
Basically, they are used any time you want to make something’s reflection look bigger
 In a shaving mirror or makeup mirror your reflection is larger so that you can perform personal grooming to a high standard.
 Concave reflectors are used in car headlights. The bulb of the head light is placed at the focal point of the reflector. The reflected light emerges in a parallel beam and gives more concentrated visibility to the driver at night.
Concave mirrors are used in solar powered gadgets. The parallel rays of the sun are reflected to focus at the focal point F. The solar energy concentrated at F is then used (usually the IR is used - heat focus) or converted (for example into electrical energy by a solar cell) by the gadget
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