WOLFRAM NOTEBOOK

WOLFRAM|DEMONSTRATIONS PROJECT

Lensmaker's Equation

​
refractive index n
1.65
thickness of lens d
0.5
curvature
1
R
1
0.3
curvature
1
R
2
-0.3
The lensmaker's equation relates the focal length of a simple lens with the spherical curvature of its two faces: ​​
1
f
=(n-1)
1
R
1
-
1
R
2
+
(n-1)d
n
R
1
R
2
,where
R
1
and
R
2
represent the radii of curvature of the lens surfaces closest to the light source (on the left) and the object (on the right). The sign of
R
i
is determined by the location of the center of curvature along the optic axis, with the origin at the center of the lens. Thus for a doubly convex lens,
R
1
is positive while
R
2
is negative.
The focal length
f
is positive for a converging lens but negative for a diverging lens, giving a virtual focus, indicated by a cone of gray rays.
The lens index of refraction is given by
n
. Optical-quality glass has
n
in the vicinity of 2.65. The top slider enables you to vary
n
between 1.0008, its value for air, and 3.42, the refractive index of diamond.
The width
d
represents the distance between the faces of the lens along the optical axis. The value of
R
2
is restrained by the slider so that the lens faces never intersect anywhere.
The parameters
d
,
R
1
,
R
2
, and
f
are to be expressed in the same length units, often cm. The reciprocal
1/f
is known as the optical power of the lens, expressed in diopters
(
-1
m
)
. A converging lens, as shown in the thumbnail, can serve as a simple magnifying glass.
In the thin-lens approximation, the lens width
d
is small compared to the other lengths and the lensmaker's equation can be simplified to
1
f
=(n-1)
1
R
1
-
1
R
2
.
Wolfram Cloud

You are using a browser not supported by the Wolfram Cloud

Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.


I understand and wish to continue anyway »

You are using a browser not supported by the Wolfram Cloud. Supported browsers include recent versions of Chrome, Edge, Firefox and Safari.