Which of the following concave
lenses has the shortest focal length? (A), (B), (C), or (D).
Before we start to tackle this
question, let’s remind ourselves of what is meant by the focal length of a concave
When parallel rays of light reach a
concave lens, the lens causes the rays of light to spread out, or diverge. Once they’ve passed through the
lens, they’re no longer parallel to each other, and the distance between each ray of
light increases as the distance of the light from the lens increases. If we look at these diverging light
rays, we might notice something interesting. If we trace each of these rays
backwards, ignoring the lens, it appears as though all of the rays come from a
single point. We call this point the focal
Note that the actual light rays
don’t all physically pass through this point. It just appears that they come from
this point, because of the way the lens has caused the rays to spread out. The focal length of a lens is
defined as the distance between the focal point and the center of the lens.
In this question, we are asked to
identify the concave lens that has the shortest focal length. Before we can do that, we need to
understand why concave lenses with different shapes have different focal
lengths. Concave lenses of different shapes
have different focal lengths because they cause parallel light rays to diverge by
different amounts. For example, let’s look at two sets
of light rays which have each been passed through different-shaped concave lenses
and hence are diverging by different amounts. If we compare these two sets of
light rays, we see that the light rays on the right-hand side have been spread out
much more than the light rays on the left.
Now, let’s trace the rays back and
mark the focal points and focal lengths of each lens. If we compare these two diagrams,
we see that the lens on the right has a much shorter focal length than the lens on
the left. This is because this lens causes
the light to diverge more, so it appears that the light is coming from a point
closer to the lens. So we have seen that the lens that
causes the light rays to diverge the most has the shorter focal length.
To answer the question we have been
asked, we need to identify the lens that has the shortest focal length. This will be the lens that causes
light rays to diverge the most. At first glance, these lenses all
appear very similar. All of the lenses are concave and
so have the same kind of shape. Each lens is thicker at the top and
bottom than it is in the middle, and each lens has a smooth curve along either
However, when we look closer, we
see that the lenses do in fact have different shapes. The edge of the lenses curve by
different amounts. This lens here has the most
significant curve, and this lens here has the least significant curve. So which of these lenses will cause
light rays to diverge the most and hence have the shortest focal length?
Well, the curve along the edge of
the lens is actually what causes the light rays to diverge. So it makes sense that the lens
with the most significant curve will cause the light rays to spread out the most and
hence will have the shortest focal length. For example, if parallel light rays
were to pass through a rectangular prism, with no curved edges, the light rays would
still be parallel after they had passed through the lens. They would not diverge at all.
When parallel light rays pass
through a lens that is slightly concave, like option (B), the rays will diverge
slightly. When parallel rays pass through a
lens that is very concave, like option (A), they will diverge much more. This means this lens will have a
much shorter focal length. Out of the options we’re given,
lens (A) has the most significant curvature. Hence, lens (A) will cause the
greatest divergence of parallel light rays. This also means that lens (A) will
have the shortest focal length. So the correct answer to this
question is option (A).