Geometric Optics

Rays and Wave fronts

Light is a very complex phenomenon, but in many situations its behavior can be understood with a simple model based on rays and wave fronts. A ray is a thin beam of light that travels in a straight line. A wave front is the line (not necessarily straight) or surface connecting all the light that left a source at the same time. For a source like the Sun, rays radiate out in all directions; the wave fronts are spheres centered on the Sun. If the source is a long way away, the wave fronts can be treated as parallel lines.

Definition provided by Boston Univeristy f    = Focal length

d0 = Object distance

di  = Image distance

for Spherical Mirrors

f = R/2

f  =  Focal length

Real images

In optics, a real image is a representation of an object (source) in which the perceived location is actually a point of convergence of the rays of light that make up the image. If a screen is placed in the plane of a real image the image will generally become visible on the screen. Examples of real images include the image seen on a cinema screen (the source being the projector), the image produced on a detector in the rear of a camera, and the image produced on a human retina (the latter two pass light through an internal convex lens).

In ray diagrams (such as the images on the right), real rays of light are always represented by full, solid lines; perceived or extrapolated rays of light are represented by dashed lines. A real image occurs where rays converge, whereas a virtual image occurs where rays only appear to converge.

Real images can be produced by concave mirrors and converging lenses.

When we look into a convex mirror or see through a concave lens, what we see is not a real image. This image, which appears to be on other side of the lens or mirror plane, is known as a virtual image

Definition provided by Wikipedia

Example of a Real image Unlike the virtual example, these lenses and mirror have rays that meet at a single point, as a matter of fact, all light rays coming from the tip of the arrow meet at that point.

Lenses and mirrors that behave this way are called converging because the rays converge at a point.

Virtual Images

In optics, a virtual image is an image in which the outgoing rays from a point on the object always intersect at a point. A simple example is a flat mirror where the image of oneself is perceived at twice the distance from oneself to the mirror. That is, if one is half a meter in front of the mirror, one's image will appear to be at a distance of 1 meter away (or half a meter inside or behind the mirror).

To contrast, a real image is an image in which the outgoing rays from a point on the object pass through a single point. It is easiest to observe real images when projected on an opaque screen. A screen is not necessary for the image to form.

Definition provided by Wikipedia

Example of a virtual image As you can see, the solid blue lines are rays of light.  In the top image the rays of light pass through the len and are bent away from each other never crossing each other.  It's only when trace the lines back do they intersect each other.

In the second diagram the light bounces of the surface of the mirror and reflect back away from each other never crossing each other.  It's only when trace the lines back do they intersect each other.

Both the lens and the mirrors they behave like the example above are called diverging because the rays diverge from each other.

Focal Point and Focal Length

Focal Point

Two points on the axis of a mirror or lens, one point being such that rays diverging from it are deviated parallel  to the axis upon refraction or reflection by the system and the other  point being such that rays parallel to the axis of the system converge to the point upon refraction or reflection by the system.

F is the focal point, where incoming parallel rays of light converge to a point (either real rays, like the top image and the third image.  Or virtual rays like the second image and the bottom image).

f is the focal length the distance from the center of the lens or mirror to the focal point

A second focal point and focal length is located on the other side of the lens or mirror.  For thin lenses and mirrors these secondary focal points and lengths have the same value. Focal length

For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot. For a diverging lens (for example a concave lens), the focal length is negative, and is the distance to the point from which a collimated beam appears to be diverging after passing through the lens.

For mirrors (spherical mirrors only) the focal length is half the radius of curvature

f = R/2