Nikon's DX lenses are another answer to matching a sensor, just like the Olympus E-System lenses. As you can see below, the image circle of a Nikon DX lens is smaller than that of a 35mm lens image circle.

Since the image circle is smaller, it captures more of the image than a 35mm lens on a Nikon DX Sensor. However, since the imager is smaller than a 35mm imager, your Field Of View is going to be much different.