Ray Diagrams

This Java applet demonstrates how to draw ray diagrams for spherical lenses and mirrors.

Theory

First, a coordinate plane is drawn with the mirror or lens placed vertically. The center of the optics of the mirror or lens is placed at the vertex. The horizontal axis is called the principal axis.

Spherical mirrors

A concave mirror has a positive radius and focal length. The radial point is drawn on the principal axis on the same side as the object. A convex mirror has a negative radius and focal length; the radial point is drawn on the principal axis on the other side of the mirror from the object.

The ray diagram is as follows:

Draw a line from the top of the object (object distance and object height) through the vertex.
Draw a second line with the opposite slope through the vertex.
The third ray is drawn from the object through the radial point.

The point at which the third ray and one or the other of the first two rays intersect is where the image will appear. If the image is in front of the mirror (the same side as the real object), it is real and its distance is positive. If the image is back of the mirror, it is virtual and its distance is negative.

Spherical lenses

A biconvex lens has a positive focal length; a biconcave lens has a negative focal length. The focal points are drawn on the principal axis on both sides of the lens.

The ray diagram is as follows:

Draw a line from the object through the vertex.
Draw a second line from the object to the lens, parallel to the principal axis.
Draw a third line from the object through the focal point. For a positive focal length, use the focal point on the side of the lens opposite the object. For a negative focal length use the focal point on the same side of the lens as the object.

The point at which the first and third rays intersect is where the image will appear. If the image is in back of the lens (the opposite side of the from real object), it is a real image and its distance is positive. If the image is in front of the lens, it is virtual and its distance is negative.

Mirror Equation:

$1/f = 2/r = 1/p + 1/i$

Thin Lens Equation:

$1/f = 1/p + 1/i$

Lens Maker's Equation:

$1/f = (n2/n1 - 1)*(1/R1 - 1/R2)$

Magnification:

$m = -i/p$
$|m| = h'/h$

p: object distance
i: image distance
h,h': object and image height
f: focal length
r,r1,r2: radius
n1: index of refraction for surrounding medium
n2: index of refraction for lens material

Use the Restart/Step button to view each ray trace in sequence.
The Lens/Mirror selection buttons switch between a lens and a mirror.
Each of the fields has a small check box next to it that allows you to lock the value of that field.

Please send all comments, criticisms, suggestions to medgar@student.gc.maricopa.edu (Mark Edgar)