### Video Transcript

The diagram shows five light rays
that will pass through a thin convex lens. Which of the light rays will not
change direction as it passes through the lens?

Here, we are given a diagram of a
convex lens with five rays of light that will pass through it. We are asked to figure out which
ray will not change direction when it passes through the lens. Let’s begin by refreshing our
memories about what a convex lens is and how light rays behave when passing through
them.

First, let’s look at the shape of a
convex lens. As viewed from the side, it can be
created by overlapping two circles and taking the section in the middle. We can see that our lens is
thinnest along the edges, while it is thickest in the middle of the lens. This shape allows convex lenses to
focus light rays as they pass through and make them converge at a point on the other
side of the lens. Light rays that are parallel to the
optical axis but not on it will have their directions changed and be bent towards
the optical axis and converge at a point called the focal point.

Now, let’s take a look at the
center of the lens. And notice that it is aligned with
the center of curvature of each of the circles that determine the shape of the
lens. A center of curvature of a circle
is a point that is at equal distance from every point on the circumference of a
circle. This distance is called the radius
of curvature, and it equals the radius of the circle.

If we connect the centers of
curvature with a line, this line passes through the center of the lens and it
defines the optical axis of the lens. If we take the point on the optical
axis that is at the center of the lens, it is a special point in a convex lens. If any light rays pass through this
point, they will pass through without changing direction. Knowing this, we can look at the
diagram in the question and find the ray that passes through the point along the
optical axis at the center of the lens.

Looking at the five rays we are
given, ray one and ray two are above the optical axis, while ray four and ray five
are below the optical axis. These rays all travel horizontally
parallel to the optical axis, which means they cannot pass through the center of the
convex lens and instead will be focused and pass through the focal point on the
other side of the lens to the side that they entered the lens from. Ray three travels along the optical
axis and so will pass through the center of the lens. Ray three then will not change
direction while passing through the lens. Ray three is the correct
answer.