The exercise required that we photograph a piece of fruit while keeping the camera to subject position constant and the light to subject angle constant. Light size and distance was varied.The first image was taken with a bare flash 300mm from the apple at 70 degrees to the camera and slightly above. This is the smallest apparent light size in the examples. The shadow is clearly defined and the light would definitely be described as hard. The highlight from the flash can be seen on the apple.
The second image was taken with the strobe 600mm away. I have failed slightly by not keeping the vertical angle to the subject constant. This has resulted in a lengthening of the shadow. It is however possible to see that the shadow to light transition area (penumbra) is shorter. The shadow edge is sharper. With the increase in distance the apparent light size is even smaller.
Image three has the flash even further away at 1500mm. Again the shadow is lengthened due to decreased vertical angle but this is not the point of this exercise. The apparent light size here is the smallest in all of these examples and yields the sharpest penumbra. The shadow is not as dark but this is because I opened the camera aperture rather than increase the flash power to keep the exposure correct. The ambient light has therefore lightened the shadow slightly.
Image three has the flash even further away at 1500mm. Again the shadow is lengthened due to decreased vertical angle but this is not the point of this exercise. The apparent light size here is the smallest in all of these examples and yields the sharpest penumbra. The shadow is not as dark but this is because I opened the camera aperture rather than increase the flash power to keep the exposure correct. The ambient light has therefore lightened the shadow slightly. 
The second three images are taken using a white translucent umbrella. The flash is shot through the umbrella. The first image is again the closest at 300mm. Comparing this with the bare flash is very instructive. The apparent light size here is the biggest of all the examples. There is still a shadow but it is minimal and the real difference is the very gradual change from light to shadow. Also of significant note in this image is the hardly noticeable highlight. It is hardly noticeable because it is so large. The other very significant point here is the less well defined transition from light to shadow on the body of the apple itself. Clearly, in the case of portrait photography this is desirable. There is enough of a difference to create the impression of three dimensions without harsh shadows cast by facial features.
The final two images show the increasing shadow due to vertical angle change again (not the point of this exercise!). They also show the light to shadow transition becoming slightly harsher again.
Even though we have a 115cm diameter light source, as it gets further away it's apparent size is reducing even though it is still big compared to the bare flash.
The most extreme example of apparent light size from a photographers point of view is the sun. It is also the most commonly used light source! The sun is the biggest light source a photographer will ever use but paradoxically it normally supplies some of the hardest light. The reason for this is the 93 million miles that lies between the source and the subject. It can of course supply very soft light but this will be because of cloud or fog or some other atmospheric effect. This is in effect adding a very large umbrella or softbox.
