Ever wonder about the laws of optics, and how a camera lens actually works? These questions and more will be answered in the following article, both for pros and those with an interest in photography.
What are you waiting for? Let’s go!
How a camera lens creates an image?
An optical system can converge the light emitted by an object to create a projected image of that object. An image created in this way has two fundamental characteristics:
- It’s real: you can see it can on a screen
- It’s turned upside down and sideways
This happens with any optical system. Be it a pinhole, a simple lens, or even ta camera lens, a complex set of lenses. Even our eyes work in the same way.
As you can see, it’s not important what type of camera you use. You can shoot with a full-frame sensor digital camera, a film camera, or a large-format one. You can use a long or a short focal length. Optics don’t care, the image will always be translated and upside down.
A lens is any transparent medium delimited by two surfaces of which at least one is curved.
When lenses are thicker in the center than at the edges, they are positive lenses.
The refraction of incident light radiation causes the latter to converge from the opposite side of the lenses themselves.
From the two surfaces of a positive lens, one must be convex, while the other can be either flat or concave or also convex.
When the surfaces are both curved, it is possible to identify their centers of curvature.
The optical axis is the line that passes through these two points.
Note: Planoconvex lenses have a curved and a plane surface. The optical axis is the straight line passing through the curvature’s center of the curved surface. Which intersects the plane perpendicularly in its center.
Inside the camera lens
To learn about camera lenses, depth of field, and photography in general, it’s really important to know some principle about optics.
In my opinion, the best way is to learn the principal definitions of optics.
The optical center is the point where any light emanating from a lens will not deviate from its course.
It is not necessarily within the physical dimension of the lens.
Every lens has a front nodal point (object nodal point), and a back nodal point (image nodal point).
When a ray of light enters the object nodal points, it comes out as if it came from the image nodal point, and vice-versa.
Nodal planes are the two planes, parallel to each other and perpendicular to the optical axis, to which the nodal points belong.
Time to simplify!
As photographers, we do not need to know all the Gauss optical theory. We can simplify it, making the nodal points and nodal planes correspond, to the points and the planes of the object and the image. Even if it’s physically untrue, we can consider the cones of light refracted by a lens, having their bases on these planes.
Thanks to this simplification, we can easily calculate the conjugated points and the reproduction ratio.
The final result will be approximated for an irrelevant amount, and it’s applicable to every camera lens you use.
The main focus point
Incident radiation comes from an object-point placed on the optical axis at a great distance from a lens (in photography is called infinity ∞). For this reason, they can be considered parallel. The refraction of a positive lens leads them to always converge and intersect on the optical axis.
That point is called the image main focus point ( or back main focus). Its distance from the back nodal point is called focal length (f).
In addition to what has been said, each positive lens also has a front main focus point and a front focal length. They can be calculated with the same procedure applied above but with light radiations coming from behind the lens.
Negative lenses are thicker at the edges than in the center. They make incident rays of light diverge. These lenses cannot produce image points as positive ones do. It is possible to identify a virtual main focus and focal length using the extensions of the refracted radiation in front of them.
The graphic construction of a camera lens
Now it’s time to create a representation based on a few fundamental notions. This is basically how a camera lens works.
Geometric optics, allows us to consider electromagnetic waves as if they were simple straight lines. It is far from physics and quantum optics but is enough for our needs.
Incident rays of light on the lens may have 3 possible behaviors:
- A ray of light passing through the center of a lens is not deflected but only translated
- When a ray of light is parallel to the optical axis, it is refracted by a lens to meet the optical axis in the back nodal point
- A ray of light that reaches the lens through the front main focus is refracted until it is parallel to the optical axis
The theory of conjugate points and the lens magnification
In the previous figure, the letters o and i represent the conjugate points. The conjugate points are the distances between a point of the subject and the front nodal plane (o) and that between the back nodal plane and the image point produced by the lens (i). These distances are called conjugates points because they vary proportionally according to the focal length of the camera lens itself. In this case, the greater the distance o, the smaller the i, and vice versa.
These concepts are also expressed by the formula:
From which we can obtain:
Whereby with M we mean the magnification: the ratio between the desired size of the image and the subject (o and i).
These formulas allow you to calculate:
- The distance from the subject (o) needed to reproduce it in a certain size
- The distance between the lens and the sensor required to have a specific magnification.
Time to simplify again
A further simplification of these concepts is possible through the subdivision of the normal shooting conditions into some categories:
- When the subject is at a very large (infinite) distance, his image is at a distance equal to the focal length of the lens.
- When the subject is at a distance between infinity and twice the focal length of the lens, his image will be a distance between one and two focal lengths; this image will be real, upside down is overturned. The playback ratio will be less than one.
- When the subject is at a distance equal to twice the focal length of the lens his real, flipped, and upside-down image, will also be at a distance equal to twice the focal length, and the reproduction ratio will be 1:1
- When the subject is at a distance between two times and once the focal length of the lens, his real, flipped, and upside-down image, will be at a distance between twice the focal length and infinity, the reproduction ratio will be greater than one
- When the subject is at a distance equal to a focal length, his real, flipped, and upside-down image will be at the infinite, and will therefore be infinite in size.
Is evident that some of these situations occur in practice.
When you increase the distance from the object, the exposure decrease according to the inverse square of that distance variation.
Don’t forget to correct the exposure, especially if the camera lens magnification ratio is greater than 1:10.