Refraction: Points and
Planes
Basic Optics, Chapter 18
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Understanding Focal Points and Planes in Optics, Schemes and Mind Maps of Optics
An in-depth exploration of the concept of focal points and planes in optics. It explains the significance of primary and secondary focal points, primary and secondary focal planes, nodal points, and lens axes. The document also discusses the difference between thin and thick lenses and how they affect the location of these important points.
Typology: Schemes and Mind Maps
2021/2022
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Refraction: Points and
Planes
Basic Optics , Chapter 18
As we learned in Chapter 4, every lens has two
focal points:
the primary focal point
the secondary focal point
Points and Planes
As we learned in Chapter 4, every lens has two
focal points:
the primary focal point
the secondary focal point
And as we shall see shortly, these points are
simply special locations on two important planes:
the primary focal plane
the secondary focal plane
But first we will meet several other important
members of the light-ray model family:
the nodal point (s)
the lens axis
Points and Planes
Object
Object
Image
Image
Primary focal point
Secondary focal point
Primary focal point: Location at
which an object could be placed,
and light rays associated with the
object would exit the lens with zero
vergence (i.e., parallel)
Secondary focal point: Location at
which the image is formed when
light rays with zero vergence (i.e.,
parallel) encounter a given lens
As we learned in Chapter 4, every lens has two
focal points:
the primary focal point
the secondary focal point
And as we shall see shortly, these points are
simply special locations on two important planes:
the primary focal plane
the secondary focal plane
But first we will meet several other important
members of the light-ray model family:
the nodal point (s)
the lens axis
Points and Planes
As we learned in Chapter 4, every lens has two
focal points:
the primary focal point
the secondary focal point
And as we shall see shortly, these points are
simply special locations on two important planes:
the primary focal plane
the secondary focal plane
But first we will meet several other important
members of the light-ray model family:
the nodal point(s)
the lens axis
The primary focal points, nodal points, and two others called the principal points (which, you will be happy to learn, we won’t get into) comprise what are known as the cardinal points for a lens system. Taken together, the cardinal points capture and describe the critical optical properties of any lens system. (And that’s all I think you need to know about cardinal points per se .)
We’ll address the reason for this waffling shortly
Points and Planes
F 1 F 2
Thin plus lens
Primary focal point Secondary focal point
Points and Planes Note: The term thin here means infinitely thin. Obviously, real lenses are not infinitely thin! A thin lens is a theoretical construct we employ because it simplifies the optics and thereby facilitates understanding.
F 1 N F 2
Thin plus lens
Primary focal point Secondary focal point
Nodal point (N): Location through which any ray, from any angle, will pass undeviated
If a ray passes through the nodal point, it will not be refracted-- that is, it will exit the lens with the same angle at which it entered
Points and Planes
F 1 N F 2
Thick plus lens
Primary focal point Secondary focal point
θ N
???
As an important aside…
Points and Planes
In a thick (i.e., real) lens, there are two nodal points. However…the same rule applies—a ray entering one nodal point will appear to ‘jump’ to the other and exit at the same angle (i.e., undeviated)
F 1 F 2
Thin plus lens
Primary focal point Secondary focal point
(Technically speaking, a thin lens has two nodal points as well—it’s just that they are both located at the same point in optical space.)
N
N
Points and Planes
F 1 N F 2
Thin plus lens
Primary focal point Secondary focal point
Lens axis : The ray that passes through both focal points and the nodal point
Points and Planes
F 1 F 2
Thin plus lens
Primary focal point Secondary focal point
Lens axis : Passes through both focal points and the nodal point
N
Optical
Points and Planes
The term optical axis is more general, and can be applied to eyes as well as lenses. (Recall from Chapter 4 that eyes have focal points; trust me that eyes also have nodal points.) Bonus question : As shown, is this an emmetropic , hyperopic or myopic eye? Hyperopic. (The tipoff: The secondary focal point is behind the eye.)
F 1 F 2
Thin plus lens
Primary focal point Secondary focal point
Lens axis : Passes through both focal points and the nodal point
N
Points and Planes
The term optical axis is more general, and can be applied to eyes as well as lenses. (Recall from Chapter 4 that eyes have focal points; trust me that eyes also have nodal points.) Bonus question : As shown, is this an emmetropic , hyperopic or myopic eye? Hyperopic. (The tipoff: The secondary focal point is behind the eye.)
Optical
F 1 F 2
Thin plus lens
Primary focal point: The location from which rays hitting a lens will leave that lens with zero vergence (i.e., parallel to lens axis). You know this from Chapter 4.
N
Points and Planes
F 1 F 2
Thin plus lens
N
Primary focal plane : Rays emanating from any point on this plane will exit the lens parallel to one another (but not necessarily parallel to the lens axis)
Points and Planes