Basic lenses and mirrors come in two different kinds: concave and convex. These types differ in how and where they focus light. A concave lens diverges light—scatters it and cannot bring it into focus—and the ‘image’ that it forms shows up on the same side as the light it is reflecting. That is because the focal point, which is the point where light rays come to focus or meet, is on the same side of the lens as the light source. The distance between the lens and the focal point is considered to be a negative focal length. You can demonstrate this with a small concave lens: hold the lens over a piece of paper on a table or countertop, near a source of natural light, such as sunlight coming through a window. A small beam of tinted light (the virtual image) should appear on the paper on the same side of the lens as the light is coming from. You can think of it as light bouncing back from the surface of the lens, instead of going through it.
The focal point and image (called a real image) of a convex lens appears on the opposite side of the light it is reflecting. The distance between the lens and the focal point is a positive focal length. You can demonstrate these properties by using a convex lens in the same setup you used for the concave one. This time, the image from the light should appear on the opposite side of the light source.
Mirrors work in a similar way. If you have a small concave mirror, hold it so that light is reflected off of it onto a screen (a manilla folder or a light-colored notebook works well). Now, hold your finger in front of the mirror, without covering the entire surface. Since light diverges off concave mirrors, the image of your finger will not appear on the screen.
Try the experiment again with a convex mirror. The image of your finger (looking like a shadow) should show up on the screen. Unlike concave mirrors, convex mirrors project a clear image. This enables us to see an accurate (though reversed) image of ourselves when we look in a convex bathroom mirror.