Ray diagrams/tracing lenses:
Lenses are transparent materials that have been shaped to bend light in specific ways. Lenses take
on a variety of shapes which depend on their function and what direction light is needed to bend.
We will be referring to biconcave and biconvex lenses in this module (concave or convex on both
sides of the lens).
Like mirrors, these lenses are either converging or diverging.
Biconvex lenses are converging (bend light to a single focus point):
Biconcave lenses are diverging (bends light away)
Ray diagrams:
Just like with mirrors, it is helpful to draw ray diagrams to determine how these lenses form images
and what properties these images will have. Let’s consider convex lenses first:
There are 3 rules that we follow when drawing ray diagrams for convex lenses:
Rule 1: a ray travelling parallel to the principal axis will be refracted to the focus on the other side
of the lens
Rule 2: a ray travelling through the optical centre of the lens will not be bent and will travel along
the same path
Rule 3: a ray travelling through the focus will be refracted to travel parallel to the principal axis on
the other side.
We need to choose 2 out of the 3 rules to determine where the image will be formed.
Note: points along the principal axis are a little different with lenses – F1 and F2 are the 2 focal
points of the lens (there is 2 because light can travel from both directions with lenses. 2 F1 and 2 F2
are the points where the focal length is doubled.
Task 1:
-
Draw the ray diagrams of an image formed from a convex lens at 3 different points and
describe the image:
object is at 2 F1
o
object is at F1
o
object is between F1 and O
o
We will now have a look at concave lenses. Again there are a few rules which apply for convex
lenses:
Rule 1 – a ray travelling parallel to the principal axis will be refracted appearing to be coming from
the focus
Rule 2 – a ray travelling through the optical centre of the lens will not refract and continue along the
same path
Rule 3 – a ray travelling towards the focus will be refracted to be parallel to the principal axis
Task 2:
-
Draw the ray diagrams of an image formed from a concave lens at 2 different points and
describe the image:
Do you notice a pattern with concave lenses? Describe this pattern or property of the image.
The lens formula:
Similar to the mirror formula, the lens formula lets us calculate the position of the image formed
from lenses. The formula is:
1 1 1
= +
𝑓 𝑢 𝑣
This formula is exactly the same as the mirror formula and the sign conventions are also similar:
-
If image distance is negative, the image is virtual
If the image distance is positive, the image is real
Magnification formula:
The magnification or size of the image can be calculated for both lenses and mirrors. This formula is
given by: h1 h0
𝑀=
ℎ1 𝑣
=
ℎ0 𝑢
Where:
-
h1 is the height of the image.
h0 is the height of the object
v is the distance between the image and the mirror
u is the distance between the object and the mirror
Task 3:
Complete 10.3 Review questions from your Pearson textbook (7 questions)