Chapter 5: Lenses
Please remember to photocopy 4 pages onto one sheet by going A3→A4 and using back to back on the photocopier
Two types of spherical lens: convex (which is also called ‘converging’ because it causes rays which are arrive parallel
to the principle axis to converge) and concave (caves in as you look at it – also called ‘diverging’).
Convex (converging) lenses – ray diagrams
You should be able to draw a ray diagram showing how an image is formed by a convex lens when the object is
(i) outside the focus – resulting in a real image
(ii) inside the focus – resulting in a virtual image
From top of object to lens (parallel to principle axis) and after passing through the lens then passes through the focal
point on the other side.
From top of object through focal point and after passing through the lens continues on the other side parallel to the
Centre of Curvature: From top of object to centre of curvature and continues straight through.
For each of the following label the focal point, the object and the image.
Put arrows on all rays, and state whether the image is real or virtual, upright or inverted, magnified or diminished
Object outside f Object inside f
Notice that when the object is inside the focal point the light rays never intersect, but from the viewer’s perspective
they appear to do so behind the mirror (the viewer is to the right of the lens in the diagrams above).
A real image is always on the other side of the lens (to the object) and is inverted.
A virtual image is always on the same side of the lens is upright.
Concave (diverging) lenses – ray diagrams
Here only one diagram is needed; the image is always diminished, upright and virtual.
(i) From top of object to the lens parallel to principle axis and up as if coming from the focal point.
(ii) From top of object to the lens as if passing through centre of curvature.
Notice that in this situation (similar to the convex mirror when the object is inside the focus) light rays never intersect,
but from the viewer’s perspective they appear to do so at the same side of the lens as the mirror.
The image is therefore always virtual, regardless of where the object is placed.
Relationship between focal length (f), object distance (u) and image distance (v)
For a convex lens f is positive
For a concave lens f is negative
For a real image v is positive
For a virtual image v is negative
The last two lines are what is referred to as the ‘Real is Positive’ convention (RiP).
Remember that for a convex lens the image is only virtual if the object is inside the focus.
For a concave lens the image is always virtual.
u is always positive for both types of lens
If you are told that v is virtual, or if it is obvious from the question (because the lens is diverging or because the object
is inside the focal length if the lens is converging) then you should make the value for v negative at the beginning of
Note: If you are told that v is virtual, or if it is obvious from the question (because the lens is concave, or because the
object is inside the focal length if the lens is convex) then you should make the value for v negative.