Video Transcript
The diagram below shows two convex
lenses. Which lens has the greater radius
of curvature?
In this question, we are shown two
circles that are of different radius to each other. Each circle has a convex lens
positioned over it so that one side of the lens exactly covers a part of the
circumference of the circle.
The question asks which of these
lenses has the greater radius of curvature. The first thing to understand is
that the radius of curvature of a lens is not the same thing as the thickness of a
lens. Lens 2 is clearly thicker than lens
1, but this does not necessarily mean that lens 2 has the greater radius of
curvature. The radius of curvature of a lens
depends on both the thickness of the lens and on the height of the lens, as it
describes how the surface of the lens curves along its length.
To better understand what radius of
curvature is, let’s recall some important facts about convex lenses. As viewed from the side, the shape
of a convex lens can be created by two overlapping circles, where the lens has the
shape of the overlapping parts of the circles. Convex lenses are thinner around
the edges of the lens and reach their thickest point in the center of the lens along
the optical axis. Remember that the optical axis is a
straight line that passes through the center of curvature for the two circles right
through the center of the lens. The two centers of curvature for a
convex lens are the centers of curvature for the overlapping circles that make its
shape.
The center of curvature for a
circle is the point in a circle that is equal distance to every point along the
circumference on the circle. The line that connects the center
of curvature and the circumference of the circle is called the radius of
curvature. We can see that this line has the
same length whichever point on the circumference of the circle it connects to. We can see that for a circle, the
radius of curvature is simply the radius of the circle and the center of curvature
is simply the center of the circle. This means that the radius of
curvature of a convex lens is equal to the radius of curvature of the circles that
were overlapped to make the shape of the lens.
Now for both lens 1 and for lens 2,
let’s look at one of the two circles that were overlapped to make the shape of each
lens. We can then compare the radii of
curvature of these circles. Notice that the circle for lens 1
is larger than the circle for lens 2. A larger circle has a greater
radius. As the radius of curvature of a
circle is simply the radius of the circle, the circle for lens 1 must have the
greater radius of curvature. Recall that the radius of curvature
of a convex lens is equal to the radius of curvature of the circles that were
overlapped to make the shape of the lens.
We have just seen that the circle
for lens 1 has the greater radius of curvature, so lens 1 must also have the greater
radius of curvature. So lens 1 is the correct
answer.
