How do you identify converging vs diverging lenses from principal rays?

[rei]

I got a problem where it gives us a diagram with a lens, a source and a image. We have to draw the three principal rays. But after drawing the rays, how can I tell if it is a diverging or converging len? And how can I explain it verbally? Thanks a lot!

 

[rei]

Can anyone give me a hint please?

 

[mikeu]

After the rays pass through the lens, do they meet at a single point or spread away from each other? In general, a convex lens will cause them to converge to a point on the opposite side of the lens as the object, whereas a concave lens will cause them to diverge away from a point on the same side as the object.

 

[rei]

The problem doesn't give me the focal point. If the source is inside the focal point, the image can be on the same side of the source in the case of the converging lens too. So how can I tell? Thanks!

 

[HallsofIvy]

Draw a picture. Represent the lens as a single vertical line. Represent your object as an arrow, also vertical, and mark the focal points on either side of the "lens" as single points in line with the center of the "lens". Draw two lines from the top end of your "arrow", one through the center of the lens, the other horizontal. Because the lens is symmetric (I'm assuming it is- that's the standard case), any line passing through the center of the lens with continue as a straight line. By definition of "focus", any horizontal line will bend at the lens to go through the focus. The point where those to lines converge will be the point on the image corresponding to the point on the object.

If the lens is convex then the horizontal line is bent to go through the focus on the opposite side of the lens from the object.

If the lens is concave then the horizontal line is bent to go through the focus on the same side of the lens from the object.

Doing that with the two endpoints of the "arrow" should show you what the image looks like.

Do that once for each (concave or convex) lens with the object inside the focus and once for each with the object outside the focus to see what happens.

 

[GCT]

Draw the three rays designated in your text, a ray that passes through the first focal point and then becomes parallel to the principle axis after refraction, a ray that simply passes through the center of the lens and does not refract, and a ray which is parallel initially then passes through the second focal point after refraction. You can determine the direction of the ray after refraction simply by noting the normal (which is the radial line pertaining to the surface of refraction) and deduce from there.

 

[tot]

any lens that is thicker in the middle than at the edges is a converging lens.