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9.2.5: Images Again

Images in Water

Now that we have discussed two of the ways in which light rays can change direction, let us ask what the implications are for how we perceive things. Let us consider an object that is underwater, and ask how someone standing above would see it. In Example #3 from Refraction we already drew how the refracted rays would look. Our brain assumes that these rays are traveling in a straight line, so we add dotted lines showing how our brain would interpret the origin of the light waves exiting the pool.

Note that these rays are crossing all over the place! The rays don’t come back to one place, and the more rays we add the more we see that the light appears to be coming from a whole area under the water. Why when we look straight down on an object does our brain still see the object (fairly) clearly? 

The answer is that our brain can only interpret the light rays that actually hit our eyes. Placing a pair of eyes on the diagram as well, and considering only the rays that make it to our eyes will show that we would see an image:

If we look straight down on the object then it appears to be closer than it really is. You can see this quite dramatically be standing knee-deep in a swimming pool. To someone outside the pool, all points from your foot to your knee appear closer to the surface than they really are, while the rest of you appears normal. This leads to you looking very disproportionate!

Images in Mirrors

Mirrors can be used to form images as well. Consider an arrow being reflected in a flat mirror. We draw some light rays from the head of the arrow and use the law of reflection to see where they go. We do the same for the bottom of the arrow. We notice that if we trace the reflected rays back, all the light rays from the top seem to be coming from a single point behind the mirror (this tracing is shown with a dotted line in the figure on the left). We have formed an image of the top of the arrow. We see that all the light from the bottom of the arrow seems to come from another point.

 

You should check that the rays shown on the left hand side obey the law of reflection. What does this mean? Just like the case of an object immersed in water, the light rays that bounce off the mirror are spreading out, but when our brain traces them back they all seem to be coming from the same place – we have formed an image! One way of thinking about this is that our brain could not distinguish between seeing an arrow and its reflection, or there being two arrows. The light that reaches our eyes would be exactly the same in both cases!

To show that the light rays from the image are the same as the ones produced by the mirror, compare the outgoing light rays reflected off the mirror with the outgoing light rays of a hypothetical arrow where the image is. We see that the light rays are the same.

A Complex Example: The Corner Mirror

To solidify our understanding of images in mirrors, let us consider a slightly trickier example. We will consider a point object between two mirrors at right angles as shown below. What would we see?

To simplify this problem, let us consider only the lower mirror first. Doing the ray tracing we find the location of the image for the lower mirror.

Now here comes the trick: the light rays that bounce off the mirror look exactly like they have come from the image. Therefore, the light rays that hit the vertical mirror are exactly the same as if we had two objects! We are going to pretend that this is really the case – we shall call our original object #1 and the image in the lower mirror object #2.  The rays from each image must be traced separately.  Below, this is done for object #1 on the left-hand side, and then object #2 on the right-hand side.

Are we done? We have to consider the possibility that the images on the right-hand side themselves have images in the lower mirror. The image from #2 is not a problem – all the reflected rays head away from the horizontal, mirror so it cannot have an extra image. The image from #1 is more problematic as rays from this image will hit the horizontal mirror.

To find if another image exists, imagine that the horizontal mirror is in place, the vertical mirror is missing and that “Image from #1” is really an object. Note this is what we would have done anyway if we had started with the vertical mirror rather than the horizontal one. Doing this we find that the image from #1 produces an image in the same place as the image from #2 so we don’t get any new images out. Now we have convinced ourselves we are done, we can draw the final solution:

When we look at this corner mirror we would think we saw four objects – the original object and the three images. While this example was a little involved, it was designed to show that insofar as the outgoing light rays are concerned an image is indistinguishable from having an object at that location.

Real Images vs. Virtual Images

In all the examples so far the light rays have appeared to come from the images, but this has been because our brain assumes that light travels in straight lines. The actual light rays do not actually meet at the location of the image. Only the projection of the light rays (i.e. assumption that the rays travel in straight lines), shown in the figure as dashed lines, actually cross at the location of the image. A point where our dotted lines appear to originate from is known as a virtual image. The other sort of image that can exist is a real image, where the actual light rays (solid lines) cross at the location of the image. We will come across examples of real images when we discuss lenses. (We note that lenses are not the only examples that can give real images; curved mirrors are also capable of giving real images.)

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