Resource Lesson
Lensmaker Equation
Printer Friendly Version
The following formula, called the
Lensmaker Equation
, is used to determine whether a lens will behave as a converging or diverging lens based on the curvature of its faces and the relative indices of the lens material [n
_{1}
] and the surrounding medium [n
_{2}
].
Usually the expression
is treated as a constant (K
_{shape}
) allowing us to work more often with the following second form of the equation:
Remember that K
_{shape}
represents the shape of the lens which remains constant regardless of the type of surrounding medium [n
_{2}
] into which the lens is used.
If this expression yields a negative value for 1/f, then the lens is diverging; a positive 1/f means that the lens is converging.
Refer to the following information for the next seven questions.
The following double convex lens (n
_{1}
= 1.52) has radii of curvatures equal to r
_{1}
= 15 cm and r
_{2}
= 10 cm.
As the light approaches the lens from the left, does the front surface have a positive or negative curvature?
As the light leaves the lens (having entered from the left), does the back surface of the lens have a positive or negative curvature?
State the values of r
_{1}
and r
_{2}
.
Calculate the value of K
_{shape}
.
What is the focal length of this lens in air (n
_{2}
= 1.00)?
What is the focal length of this lens if it were submerged in water (n
_{2}
= 1.333)?
What is the focal length of this lens if it were embedded in carbon disulfide (n
_{2}
= 1.628)?
It is the Lensmaker Equation that gives rise to our previous statements about the shapes of lenses and their functionality in air:
converging lenses
are lenses that are "thicker in the center" than on the edges (convex)
geometry
r
_{1}
> 0, r
_{2}
< 0 therefore K
_{shape}
> 0
Since
n
_{1}
> n
_{2}
and
K
_{shape}
> 0
1/f > 0 and these lenses will be converging.
r
_{1}
=
, r
_{2}
< 0 therefore K
_{shape}
> 0
diverging lenses
are lenses that are "thinner in the center" than on the edges (concave)
geometry
r
_{1}
< 0, r
_{2}
> 0 therefore K
_{shape}
< 0
Since
n
_{1}
> n
_{2}
and
K
_{shape}
< 0
1/f < 0 and these lenses will be diverging.
r
_{1}
=
, r
_{2}
> 0 therefore K
_{shape}
< 0
Power
To calculate the
power of a lens
, we use the relationship that
In this formula, the focal lengths are usually measured in meters resulting in the power of the lens being measured in a unit called a
Diopter
where 1 D = m
^{-1}
.
What is the power of the lens in the previous example while it is being used in air?
What is the power of the lens in the previous example while it is being used in water?
Lenses in close combination
When two or more lenses are nested or used in
close combination
, that is, with no space in between them, the equation to calculate the effective power of the combination is
At the end of an eye exam, a ophthalmologist has confirmed his patient's prescription with three thin lenses placed in close combination within his testing apparatus. Determine the power of the final lens his patient will need if the individual lenses have focal lengths of: 20 cm, -30 cm, and 25 cm.
image courtesy of
University of Illinois Eye Center
Related Documents
Lab:
Labs -
A Simple Microscope
Labs -
Blank Ray Diagrams for Converging Lenses
Labs -
Blank Ray Diagrams for Converging, Concave, Mirrors
Labs -
Blank Ray Diagrams for Diverging Lenses
Labs -
Blank Ray Diagrams for Diverging, Convex, Mirrors
Labs -
Determining the Focal Length of a Converging Lens
Labs -
Index of Refraction: Glass
Labs -
Index of Refraction: Water
Labs -
Least Time Activity
Labs -
Man and the Mirror
Labs -
Man and the Mirror: Sample Ray Diagram
Labs -
Ray Diagrams for Converging Lenses
Labs -
Ray Diagrams for Converging Mirrors
Labs -
Ray Diagrams for Diverging Lenses
Labs -
Ray Diagrams for Diverging Mirrors
Labs -
Reflections of a Triangle
Labs -
Spherical Mirror Lab
Labs -
Student Lens Lab
Labs -
Target Practice - Revised
Resource Lesson:
RL -
A Derivation of Snell's Law
RL -
Converging Lens Examples
RL -
Converging Lenses
RL -
Demonstration: Infinite Images
RL -
Demonstration: Real Images
RL -
Demonstration: Virtual Images
RL -
Dispersion
RL -
Diverging Lenses
RL -
Double Lens Systems
RL -
Mirror Equation
RL -
Properties of Plane Mirrors
RL -
Refraction of Light
RL -
Refraction Phenomena
RL -
Snell's Law
RL -
Snell's Law: Derivation
RL -
Spherical Mirrors
RL -
Thin Lens Equation
Review:
REV -
Drill: Reflection and Mirrors
REV -
Mirror Properties
REV -
Physics I Honors: 2nd 9-week notebook
REV -
Physics I: 2nd 9-week notebook
REV -
Spherical Lens Properties
Worksheet:
APP -
Enlightened
APP -
Reflections
APP -
The Librarian
APP -
The Starlet
CP -
Lenses
CP -
Plane Mirror Reflections
CP -
Refraction of Light
CP -
Snell's Law
CP -
Snell's Law
NT -
Image Distances
NT -
Laser Fishing
NT -
Mirror Height
NT -
Mirror Length
NT -
Reflection
NT -
Underwater Vision
WS -
An Extension of Snell's Law
WS -
Basic Principles of Refraction
WS -
Converging Lens Vocabulary
WS -
Diverging Lens Vocabulary
WS -
Lensmaker Equation
WS -
Plane Mirror Reflections
WS -
Refraction and Critical Angles
WS -
Refraction Phenomena
WS -
Refraction Through a Circular Disk
WS -
Refraction Through a Glass Plate
WS -
Refraction Through a Triangle
WS -
Snell's Law Calculations
WS -
Spherical Mirror Equation #1
WS -
Spherical Mirror Equation #2
WS -
Spherical Mirrors: Image Patterns
WS -
Thin Lens Equation #1: Converging Lenses
WS -
Thin Lens Equation #2: Converging Lenses
WS -
Thin Lens Equation #3: Both Types
WS -
Thin Lens Equation #4: Both Types
WS -
Two-Lens Worksheet
WS -
Two-Mirror Worksheet
TB -
27B: Properties of Light and Refraction
TB -
Refraction Phenomena Reading Questions
PhysicsLAB
Copyright © 1997-2016
Catharine H. Colwell
All rights reserved.
Application Programmer
Mark Acton