closest point on optical axis with an image that has „acceptable sharpness“
Alternatively, we can express the NearPoint using the magnification M :
A 5 Mega lens with f=7.2mm focal length and F-stop F2.4, focused to an object distance of 100mm then has a far point of
und einen Nahpunkt von
A 5 Mega lens with f=7.2mm focal length and F-stop F2.4, focussed to 100mm then results in
and a nearpoint of
thus we get
see also https://www.optowiki.info/blog/can-i-increase-the-dof-by-changing-the-focal-length/
The DOF is then, thus focussing to the hyperfocal distance results in the largest possible DOF.
Yet another way to express the Near-Point is to use the Hyperfocal distance H :
If the lens is then focused to some object distance OD, this OD can be expressed as fraction of H :
Then the near point is
the far point is
and the Depth of field is
This means however, that
For we get
For we get
Therefore by decreasing the OD by factor 2, the DOF decreased by factor 4.
or, equivalent :
Netwon’s Rings are a phenomenon of wave optics and occur if there is a small path difference of coherent light.
They occur for example for large spheres on a glass plate with a very small gap between sphere and plate.
Some light is reflected from the glass sphere’s surface and some is reflected from the glass plate’s surface.
Because the light is coherent, we get constructive and destructive interference.
For the gap being 1/4 Lambda, the path in the gap and back is lambda/2, which results in destructive interference. Same for path lengths in the gap of 3/2 lambda, 5/2, etc. Say, for gaps that are odd multiples of lambda 1/4.
For even multiples of lambda/4, say lambda/2 , 3/2 Lambda etc, we get constructive interference.
Say, we simply can count the bright rings. For 666nm red light for example, three rings are 1000nm = 1 micrometer, which is the length of the air gap.
Newton’s rings are used in lens production, together with interferometers to find how close the current shape is from the wanted shape.
Thus surface accuracies are given in “(Newton’s) Rings”. The less rings, the better the shape got to be (and the more expensive the lens will be). Also a diametre should be given, for example five rings in 18mm diameter.
According to ISO DIN 10110 the default specs are: Wavelength 546,07 nm, 5 Rings at at 10 mm clear aperture
Below is a version of Newton Rings occuring between a sphere under test and a reference sphere
Image formation of a lens. The values z und z’ are marked red.
The Newtonian equation is an equation of ray optics named after the English physicist Isaac Newton.
Solved for ObjectDistance we get:
Solved for ImageDistance we get:
This Newtonian Image equation is often used instead of the “lens equation”. Here z is the differences between object distance and focal length and z ‘ is the difference between image distance and focal length.
Then it’s image is to the right of the second Focal point (“-” 20 because the left of the focal point).
Then it’s image is to the right of the second focal point (“-” 10 because the left of the focal point).
The advantage of Newton’s equation is that you can determine the focal point and distances from these focal points of lenses relatively easy, while principal points can be relatively difficult to determine.
Normal lenses help to define “wide angle lens” and “telephoto lenses”:
Lenses with a focal length less than that of a normal lens is called wide angle lens.
Lenses with a focal length greater than that of a normal lens are called telephoto lens.
The Numerical Aperture (“NA”) is a measure for the resolution of a lens.
According to Snells Law, the Numerical aperture of the lens stays constant across various media :
From the NA , you can calulate the F-Number of a lens from the above equition with n about 1 and because (for small angles sin(x) is about tan(x)) to a simplified:
With the object distance increasing to infinity, the Working F# nears the F#.