### Video Transcript

The radius of curvature of a
concave mirror is five centimeters. Which one of the following
sentences correctly describes the focal length? (A) The focal length is five
centimeters and is the distance from the center of the surface of the mirror to the
focal point. (B) The focal length is 2.5
centimeters and is the distance from the center of the surface of the mirror to the
focal point. (C) The focal length is 2.5
centimeters and is the distance from the center of the surface of the mirror to the
center of curvature. (D) The focal length is five
centimeters and is the distance from the center of the surface of the mirror to the
center of curvature.

In this question, we are being
asked about the focal length of a concave mirror. Let’s recall that a concave mirror
looks like this so that the reflective surface that light is directed at is concave
in shape. This dashed line we’ve drawn on our
diagram is the optical axis of the mirror.

Now, let’s recall how focal length
is defined. The focal length of a concave
mirror is the distance from the center of the surface of the mirror, that’s this
point on the surface of the mirror where the optical axis passes through it, to the
mirror’s focal point.

In this case, we’re not told
anything about the focal point of this concave mirror directly. However, we are told that the
radius of curvature of the mirror is five centimeters. Recall that the radius of curvature
is the distance from the center of the surface of the mirror to the mirror’s center
of curvature. So, if this point here is the
center of curvature of the mirror, then we know that this distance is the mirror’s
radius of curvature, which in this case has a value of five centimeters.

We can use this information to work
out the mirror’s focal length. Let’s recall that the focal length
𝑓 is equal to half the radius of curvature, 𝑅 subscript 𝑐. Since the focal length is the
distance from the center of the mirror surface to the focal point, then this means
that the focal point of the mirror is on the optical axis and is exactly halfway
between the mirror’s surface and the center of curvature.

We know that for this mirror, the
radius of curvature is five centimeters. This tells us that the focal length
is equal to five centimeters divided by two, which is 2.5 centimeters. This value for the focal length
matches the value given in answer options (B) and (C). We can therefore reject options (A)
and (D) as these show an incorrect value for the focal length.

Option (C) claims that the focal
length is the distance from the center of the surface of the mirror to the center of
curvature. But we know that this is not the
case. This distance is the radius of
curvature of the mirror, not the focal length. Option (B) states that the focal
length is the distance from the center of the mirror to the focal point. We can identify this as the correct
definition.

We have therefore found that the
correct answer is option (B). The focal length is 2.5 centimeters
and is the distance from the center of the surface of the mirror to the focal
point.