Download Thin Lenses

What Happens When…
• Light is transmitted
through a glass shaped
like a triangle?
• Light is transmitted
straight toward a glass
shaped like a square?
What happens when we put them together?
If we soften the edges, we get a lens that converges light to a single point.
Thin Lenses
Objectives:
• Identify the basic properties of thin lenses, such as the focal point,
focal length, and the center of curvature.
• Calculate the location of the image of a specified object as formed
by a double convex and double concave lens and determine the
magnification and character of the image for each case.
• Construct ray diagrams to determine the location and nature of the
image of a given object when geometric characteristics of the
optical device are known.
Lenses!
A carefully ground or molded piece of transparent material
that refracts light rays to form an image.
• It is the believed that the earliest
might be from 640 B.C.
– Rock lens found in Nineveh.
• More commonly used beginning in
the 11th century.
– Reading stones
Glasses replaced reading stones in the 13th century.
Types of Lenses
• Lenses differ in terms of their shape and the materials
from which they are made.
– They typically have a circular shape with two spherical
surfaces.
• Each surface can be convergent, divergent, or planar.
• We are going to only look at double lenses.
– Convergent is a biconvex lens.
– Divergent is a biconcave lens.
Similar To The Mirrors!
• Convergent
– Light from a distant source is concentrated at the focal point.
Remember! Light from a distant source is assumed to be parallel!
Similar To The Mirrors!
• Divergent
– Light from a distant source looks like it comes from the focal
point.
Double The Fun!
• Each lens within a double lens has its own radius of
curvature and its own focal length.
• The focal lengths of each lens DOES NOT have to be
the same.
– To keep it simple, we will only look lenses where the focal
lengths are equal.
Where’s The Image?
• To find an image for a lens, we construct ray diagrams
like we do with mirrors.
– Since a lens is made out of glass, the rays of light pass through
the lens and refract.
• When describing an image for a lens, we use the same
three characteristics we used for mirrors.
Enlarged or reduced
Inverted or upright
Virtual or Real
• When does a real image form?
– When the rays of light converge on the side of the lens
opposite the source of light.
Constructing Ray Diagrams
Where the three rays
intersect is the location
of the image.
R
R
•M<1
• Inverted
• Real
Ray 1: Drawn parallel to central axis and refracted through the
focal point of Lens 1.
Ray 2: Drawn through the focal point of Lens 2 and refracts
parallel to the central axis.
Ray 3: Drawn straight through the center of the lens.
Constructing Ray Diagrams
Where the three rays
intersect is the location
of the image.
R
R
•M>1
• Upright
• Virtual
Ray 1: Drawn parallel to central axis and refracted through the
focal point of Lens 1.
Ray 2: Drawn in line with the focal point of Lens 2 and refracts
parallel to the central axis.
Ray 3: Drawn straight through the center of the lens.
Constructing Ray Diagrams
Where the three rays
intersect is the location
of the image.
R
R
•M<1
• Upright
• Virtual
Ray 1: Drawn parallel to central axis and refracted away in line with
the focal point of Lens 2.
Ray 2: Drawn toward focal point of Lens 1 and refracts parallel to
the central axis.
Ray 3: Drawn straight through the center of the lens.
Analytical Methods
• Assuming that f1= f2
Lens Equation:
1
1
1
+
=
do
di
f
Convergent: f = positive
Divergent: f = negative
Magnification (M):
hi
-di
M=
=
ho
do
• Sign Conventions:
– Height of the object (ho) is always positive.
• If image height is positive, it is upright.
• If image height is negative, it is inverted.
– Distance of object (do) is always positive.
• If the image distance is positive, it is real and on the opposite side of
the lens from the object.
• If the image distance is negative, it is virtual and on the same side of
the lens as the object.
Let’s Do An Example!
• You are taking a picture of a 7.6 cm flower that is 1.0
meter away. If your camera has a double convergent lens
with a focal length of 50.0 mm, find the…
– 3 characteristics of the image
– Position of the image
– Size of the image
Draw a Ray Diagram!!
Solve it!
• Info:
– ho = 7.6 cm
– do = 100 cm
– f = 5.0 cm
M=
hi
ho
1
1
=
-di
do
=
f
do
1
1
=
di
hi =
+
-di
do
5 cm
ho
1
1
di
di
-
=
1
f
-
1
do
1
100 cm
hi =
-(5.26 cm)
100 cm
di = 5.26 cm
(7.6 cm)
hi = -.40 cm
The image is real, inverted, and has a M<1!