Knowing the focal length of a lens is useful because it allows us to predict where light rays passing through the lens from some object will cross and form an image. The distance from the object to the lens is known as the object distance o, and the distance from the lens to the image is known as the image distance i. They are related to each other and to f by the Lens equation
1/f = 1/o + 1/i
Object distances, image distances and focal lengths can be either positive or negative. When an object is on the same side of the lens as the incoming light rays, the object distance, o, is positive. If the object is on the other side o is negative (this is caused by another lens projecting an image past the second lens...but the second lens still treats this image as its object).
Image distance works the other way around. A positive image distance means the image is on the opposite side from the incoming rays (this image is real). A negative image distance, on the other hand, means that the image is on the same side as the incoming light (this image is virtual).
6. Is there any way to have an image on the same side of a lens (of any kind of curvature) as the light source and also have the image be real? Draw it if you can conceive of a method.
7. Is there any way to have an image on the same side of a mirror (of any kind of curvature) as the light source and also have the image be real? Draw it if you can conceive of a method.