Lenses
Lenses
Focal Point
Focal
Length
Animation of Light in a
Lens
Ray Diagrams for Converging Lenses
1. Parallel incoming light is refracted through the focal
point
2. Light coming in through the focal point is
refracted out parallel
3. Rays passing through the center are
refracted out in the same direction.
4. An image is formed where the
rays cross.
A parallel beam of light is sent through an
aquarium. If a convex glass lens is held in the
water, it focuses the beam…
1. closer to the lens
than…
2. at the same
position as…
3. farther from the
lens than…
…before.
A parallel beam of light is sent through an
aquarium. If a convex glass lens is held in the
water, it focuses the beam…
The index of refraction (n)
between water and glass is less 1. closer to the lens
than…
than it is between air and
glass. Therefore the light in
2. at the same
the water bends less and if
position as…
focused farther away.
3. farther from the
lens than…
…before.
A real image is one where the light rays
actually come from the image location.
Real
Image
Virtual Image
A virtual image is one where the light
rays do not actually come from the
image location, but rather only seem to.
Lens Equations:
Distances & Focal Points:
1
p

1
q

1
f
•Focal Length for a converging lens is positive (+).

•There is something called a diverging lens which has a
negative focal length, but we have not (& will not) talk about
that type of lens.
Sign Conventions
Quantity
Object
Location
symbol Front
p
+
Back
-
Image
Location
q
-
+
Focal Length
f
+
-
Converging
Diverging (not doing
diverging lenses in this
class)
Quantity
symbol
Front
Object Location
p
+
-
Image Location
q
-
+
Focal Length
f
+
-
Object is in front of
the lens so p = +
Back
Image is behind the
lens so q = +
Real
Image
Front of lens
Back of lens
Quantity
Front of lens
symbol
Front
Object Location
p
+
-
Image Location
q
-
+
Focal Length
f
+
-
Back of lens
Virtual
Image
Image is on
front of
the lens so
q=-
Object is
in front of
the lens so
p=+
Back
Lens Equations:
Magnification
M 

h 
h

q
p
Note the
negative
sign
Signs for magnification
Quantity
symbol
Upright
Image
Image
Height
h’
+
Magnification
M
+
Inverted
Image
If M is < 1
the image is smaller than the object
If M is > 1
the image is larger than the object
Quantity
symbol
Upright
Image
Image
Height
h’
+
Magnification
M
+
Image is inverted
(upside down) therefore
h’ = -
Inverted
Image
Real
Image
The lens projects an image of the candle on a wall. How
will the image differ if the top half of the lens is covered
with a red filter and the bottom half with a green filter?
Lens