Video Transcript
The picture below shows a box of
lenses and prisms of different sizes. How many convex lenses are there in
the box?
In this question, we are given a
box with 13 lenses and prisms of different shapes and sizes. We are asked to figure out how many
convex lenses there are in this box.
To start, let’s remember what a
convex lens is and some of its properties. A convex lens has a shape that is
made by partially overlapping two circles. We can see, looking at this shape
from top to bottom, that it has a varying width. The shape is thinner at its top and
bottom ends, and it is widest at its center. It is important to understand that
we do not always see convex lenses that are vertically oriented. A convex lens might be rotated so
that its thin ends are not top and bottom, but left and right, for example.
Let’s begin looking at the 13
shapes given and determine how many of them are convex lenses. Looking at object one in the
bottom-left corner, we see that it is thinner at one end, but it is also a triangle
shape. So this is not a convex lens. Moving up slightly to object two,
we see that it is widest at the edges and thinnest in the middle. So this is also not a convex
lens. Continuing on, object three is the
same width along its whole length and is shaped like an S. So this is not a convex lens.
Looking down slightly to object
four, we see that it is thinner at both ends and thickest in the middle. Also, it is the same shape as the
overlap of two circles. So this is the first convex
lens. Object five is also thinner at the
ends, thickest in the middle, and has the shape of two overlapping circles. So this is the second convex
lens. Object six is another triangle, so
it is not a convex lens.
Object seven is a square, which is
not the correct shape of a convex lens. Now, object eight is very thin
generally. But looking carefully, we can see
that it is thinner on the ends and thicker in the middle and is the shape of two
overlapping circles. So this is the third convex
lens. Object nine is another triangle, so
it is not a convex lens. Looking at object 10, we see that
it is thicker on the ends and thin in the middle, like object two was. So this is not a convex lens.
Object 11 has all of the properties
we are looking for. It is thinner on the ends and the
same shape as the overlap of two circles. So this is the fourth convex
lens. This object is wider than we might
perhaps expect a convex lens to be. But a convex lens can be made quite
wide by overlapping a greater part of two circles. Looking at object 12, we can see it
is thicker on the ends than in the middle so is again not a convex lens. The final object, number 13, is the
same width throughout and is not the correct shape so is not a convex lens.
Looking through the box, we have
found four convex lenses. Therefore, four convex lenses is
the correct answer.
