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An object (the arrow) is in front of a diverging lens. You can drag the lens around, but the object is fixed. Moving the mouse around in the animation gives you the position of the mouse, while a click-drag will allow you to measure angle (position is given in centimeters and angle is given in degrees). Notice the rays emanating from the object, their refraction (bending), and the resulting image. In this case the image is virtual. Restart.

To determine where the image would be located and that it is indeed virtual, place the lens at x = 2 cm. Note that there are three rays that emanate from the head of the arrow.

• One ray comes off parallel to the principal axis (the yellow centerline), is bent at the vertical centerline of the lens, and then travels to the right on a line that, if continued backwards to the left, would pass through the focal point on the near side of the lens.
• One ray comes off at an angle to hit the vertical centerline of the lens on the principal axis and is unrefracted.
• One ray, which if continued to the right would pass through the focal point on the far side of the lens, is bent at the vertical centerline of the lens and comes off parallel to the principal axis.

Given these statements, can you determine the focal length of the lens? On one (or both) of the lines that if continued would pass through a focal point, click-drag the center circle of the compass tool into position over one of those lines. Now drag the green line until it is parallel to the ray and passes through the principal axis (the yellow centerline) so that the animation looks like the following image.

If the lens is at x = 2 cm, you should get the position at which the green line crosses the principal axis to be x = 1 cm or x = 3 cm, depending on which ray you choose. In either case, since the lens is at x = 2 cm, the focal length of the lens is 1 cm.

How do we determine where the image will be located? Notice that the three rays diverge. The dotted lines continue the three rays on the right of the lens backward on the left of the lens to a point where all three dotted lines converge. This is the location of the image. It is a virtual image: A screen placed at the image location would not be illuminated by the image of the object.

Illustration authored by Melissa Dancy and Mario Belloni.