Drawing the Rays

From Lumenlab

There are three rules used for ray tracing:

Rule #1: An incident ray that is travelling parallel to the principal axis will refract at the lens and pass through the focal point

Rule #2: An incident ray that passes through the focal point on its way to the lens will refract and travel parallel to the principal axis.

Rule #3: An incident ray that passes directly through the centre of the lens where the vertical plane and principal axis intersect will not refract and keep travelling in the same direction.

As mentioned in the previous paragraphs, there are an infinite number of points on an object there is as well an infinite number of rays leaving each point. Three rays are all that are needed to trace a point from the object through the lens to a corresponding point of the image. When this point is found any of the other rays can simply be drawn in to intersect at this point.

Lamp Arc:

Lets start with tracing the lamp through the fresnels to form an image of the lamp where the triplet will be positioned. Because there are two fresnels it is possible to ray trace each one separately but in can become a bit complex doing it this way. It’s much easier to consider the two fresnels as one. To do this we simply use their combined focal length and draw them as one lens. Fig 5a Shows the two fresnels as one lens with the lamp placed at the rear fresnels focal length. The first ray drawn is from the tip of the lamp arc parallel to the principal axis. Where it intersects the vertical plane it refracts so that it passes through the focal point on the other side of the lens (Rule #1).

Next we draw a ray from the tip of the arc through the focal point on same side and continue it until it intersects the vertical plane Fig 5b. Here it is refracted so that it travels parallel to the principal axis (Rule #2).

Fig 5c shows the last ray to draw is from the tip of the arc through the intersection of the vertical plane and the principal axis (Rule # 3). Just a note, only two rays are required to find the corresponding point on the image, the other ray is drawn to check for accuracy. Where all these rays intersect is where the corresponding point on the image will be. Because we used the tip of the lamp as our reference point on the object, the corresponding point of the image will be the tip as well. So the half hight and position of the lamp image has now been traced. You could go to the trouble of tracing the other half of the arc but since it is centred the arc image will just be a mirrored image of it. Fig 5d shows where the rest of the rays can travel.

LCD:

Ray tracing the LCD through the triplet is done in the same way as was done in the fresnel example, the only difference is that the LCD object is bigger than the lens so the rays that follow the three rules won’t physically pass through the lens. Fig 6a shows how the corresponding point of the image is found and fig 6b shows the rays that actually form the image.

Virtual Image:

Ray tracing the virtual image of the LCD created by the field fresnel is slightly more difficult to draw. The same rules apply but instead of the rays travelling through the fresnel lens from the object, they are extended back to form the image on the same side as the LCD. Start with a ray drawn from the tip of the LCD travelling parallel to the principal axis. Where it intersects the fresnel it will refract and travel towards the focal point. Now extend it back on the same side as the LCD (Rule #1).

Next draw the ray from the focal point and intersect the tip of the LCD and continue it to on to the vertical plane. Now draw the ray so that it travels parallel to the principal axis and extend it back to intersect the first ray drawn (Rule #2).

The last ray to draw is from the intersection of the first two rays drawn, past the tip of the LCD and on through the centre of the fresnel. (Rule #3). The intersection of all three points is where the corresponding point of the virtual image will be created.