Wize High School Grade 12 Physics Textbook > Geometric Optics
Mirrors Ray Diagrams
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Concave and Convex Mirrors
Concave (converging) mirrors gather the reflected light rays into a single point.
Convex (diverging) mirrors disperse the reflected light rays.
Concave and convex mirrors can both be imagined as surfaces cut out of a full sphere. This is why they are called spherical mirrors.
- The principal axis (or optical axis) is the straight line perpendicular to the mirror through its center.
- The center of curvature, called , is the center of the sphere that the surface is part of.
- The focal point, called , is the point where the light rays converge, and is located halfway between the center and the mirror:
where denotes the focal length, and is the radius of the sphere.
Wize Concept
For curved surfaces, the law of reflection still applies: if you draw a tangent to the surface and the normal (perpendicular) to it, the angle of incidence will be the same as the angle of reflection (relative to the normal).
Ray Diagrams
Ray diagrams are a simplified way of representing the incoming and the reflected light, useful for determining the location and properties of the image formed by the mirror.
Step 1: Draw the mirror and the principal axis.
Step 2: Label the center (where the center of the sphere would be) and the focal point (halfway to the center).
Step 3: Draw the object as an arrow.
Step 4: Beginning at the tip of the object, draw at least two out of the four special rays.
Step 5: Extend the rays until they converge: solid lines for actual light rays, and dotted lines for imaginary rays (there is no real light there, it only appears to be coming from there).
Step 6: The tip of the image will be at the intersection point of all the rays.
Special Rays
Let's illustrate the four special rays using a concave mirror:
- Parallel ray reflects through the focal point:
- Ray through the focal point reflects parallel:
- Ray to the center reflects at the same angle below:
- Ray through the center reflects back along the same path:
Applying the same rules to a convex mirror we get:
Exam Tip
With convex mirrors you always have to extend the light rays behind the mirror using dotted lines, because that's where the focal point is, and light only appears to be coming from that side.
Wize Concept
Convex mirrors always form images that are virtual, upright, smaller and behind the mirror.
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Example: Concave Mirror
Draw the ray diagram and describe the image if an object is located inside the focal point of a concave mirror.
The image is virtual, behind the mirror, upright, and larger.
Mark Yourself Question
- Grab a piece of paper and try this problem yourself.
- When you're done, check the "I have answered this question" box below.
- View the solution and report whether you got it right or wrong.
Draw the images formed by the following objects. Describe them as real/virtual, upright/inverted, larger/smaller.
