Is there a correspondence between Tilt-Angle and the angle of the Focus-Plane?

Question

Tilt lenses have their tilt-range specified in degrees, typically around ±8°. It seems that this number corresponds to how much a lens physically tilts along one axis. The effect is to tilt the plane of focus by some angle.

Can one calculate the focus plane angle from the tilt-angle of the lens?

Can we compute the lens tilt needed to tilt the focus plane to a desired angle?

Asked by Itai

Answer

Yes. The answer is given by the Scheimpflug principle: The focal plane, lens plane, and subject plane all intersect at a common line:

Thus the angle of the subject plane depends not only on the lens tilt, but the distance of the subject. As the Wikipedia article states, the angle of tilt of the subject plane, ψ, is given by:

tan(ψ) = (u'/f) sin (θ)

Where u′ is the distance along the line of sight from the center of the lens to the plane of focus, f is the focal length, and θ is the lens tilt.

Answered by coneslayer

Check more discussion of this question.

How does the quantity of elements and blades in a lens affect the optics?

Question

I am trying to get a greater understanding of how lenses work. Basically I bought this lens, the Sigma 10-20 f4-5.6:

The construction has really fascinated me. 14 Elements in 10 Groups?! What exactly does that mean? Are the elements the blades?

What does this do the optics?

If I think about a pair of glasses there is effectively just one element.

Asked by Rob

Answer

The "elements" and the "blades" are two completely different things.

An "element" is a single piece of glass in the lens. Most of what's shown on the diagram are the lens elements. Some elements are colored pink, to indicate that their shape is aspherical. Other elements are colored blue, to indicate that they are made of a special type of glass. Others are uncolored, because they're just ordinary "spherical" elements made of typical kinds of optical glass. Your eyeglasses have a single element for each eye. Generally, using more elements, and using exotic types of glass or aspherical elements, allows the designer to better correct aberrations, or optical faults, in a lens.

When two or more elements have their surfaces in contact with each other (instead of having a gap between them), they form a group.

The number of blades refers to the number of diaphragm blades, that form the aperture stop. The diaphragm is an iris that you can make bigger or smaller, to control the amount of light that can pass through the lens. The location of the diaphragm is noted in the drawing by the vertical lines near the middle of the lens, above and below the central axis.

The number of blades is not shown in the diagram. The diaphragm looks like this:

This diaphragm has 6 blades; you can see that the aperture (opening) is a hexagon (6 sides). The number of blades is one of the factors that affects the bokeh of the lens. Your eyeglasses do not have any blades, because there's no adjustable diaphragm in eyeglasses.

Answered by coneslayer

Check more discussion of this question.