So, with all that in mind, it is easy to see why the three cameras see such a difference in the brightness of the mirror. Those positioned on each side receive no reflected light rays. From their viewpoint, the mirror appears black. None of the rays from the light source is reflected in their direction because they are not viewing the mirror from the one (and only) angle in which the direct reflection of the light source can happen. However, the camera that is directly in line with the reflection sees a spot in the mirror as bright as the light source itself. This is because the angle from its position to the glass surface is the same as the angle from the light source to the glass surface. Again, no real subject produces a perfect direct reflection. Brightly polished metal, water or glass may nearly do so, however.
Breaking The Inverse Square Law?
Did it alarm you to read that the camera that sees the direct reflection will record an image “as bright as the light source”? How do we know how bright the direct reflection will be if we do not even know how far away the light source is? We do not need to know how far away the source is. The brightness of the image of a direct reflection is the same regardless of the distance from the source. This principle seems to stand in flagrant defiance of the inverse square law, but an easy experiment will show why it does not.
You can prove this to yourself, if you like, by positioning a mirror so that you can see a lamp reflected in it. If you move the mirror closer to the lamp, it will be apparent to your eye that the brightness of the lamp remains constant. Notice, however, that the size of the reflection of the lamp does change. This change in size keeps the inverse square law from being violated. If we move the lamp to half the distance, the mirror will reflect four times as much light, just as the inverse square law predicts, but the image of the reflection covers four times the area. So that image still has the same brightness in the picture. As a concrete analogy, if we spread four times the butter on a piece of bread of four times the area, the thickness of the layer of butter stays the same.
Figure 5 has a mirror instead of the earlier newspaper. Here we see two indications that the light source is small. Once again, the shadows are hard. Also, we can tell that the source is small because we can see it reflected in the mirror. Because the image of the light source is visible, we can easily anticipate the effect of an increase in the size of the light. This allows us to plan the size of the highlights on polished surfaces.
Now look at Figure 6. Once again, the large, low-contrast light source produces softer shadows. The picture is more pleasing, but that is not the important aspect. More important is the fact that the reflected image of the large light source completely fills the mirror. In other words, the larger light source fills the family of angles that causes direct reflection. This family of angles is one of the most useful concepts in photographic lighting. We will discuss that family in detail.