Examples of Length in the following topics:

 Length is one of the basic dimensions used to measure an object.
 In other contexts "length" is the measured dimension of an object.
 Length is a measure of one dimension, whereas area is a measure of two dimensions (length squared) and volume is a measure of three dimensions (length cubed).
 In the physical sciences and engineering, when one speaks of "units of length", the word "length" is synonymous with "distance".
 There are several units that are used to measure length.

 Length is a physical measurement of distance that is fundamentally measured in the SI unit of a meter.
 Length can be defined as a measurement of the physical quantity of distance.
 Many qualitative observations fundamental to physics are commonly described using the measurement of length.
 Many different units of length are used around the world.
 The basic unit of length as identified by the International System of Units (SI) is the meter.

 Let's look at the results with the aether again.If we have a rod of length $L_0$ in the primed frame what it is length in the unprimed frame.
 We have deﬁne the length to be the extent of an object measured at a particular time.

 Length contraction is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any nonzero velocity relative to that observer.
 Now let us imagine that we want to measure the length of a ruler.
 Consequently, the length of the ruler will appear to be shorter in your frame of reference (the phenomenon of length contraction occurred).
 For example, at a speed of 13,400,000 m/s (30 million mph, .0447c), the length is 99.9 percent of the length at rest; at a speed of 42,300,000 m/s (95 million mph, 0.141c), the length is still 99 percent.
 Observed length of an object at rest and at different speeds

 The ratio of force to area $\frac{F}{A}$ is called stress and the ratio of change in length to length $\frac{\Delta L}{L}$ is called the strain.
 In equation form, Hooke's law is given by $F = k \cdot \Delta L$ where $\Delta L$ is the change in length and $k$ is a constant which depends on the material properties of the object.
 Deformations come in several types: changes in length (tension and compression), sideways shear (stress), and changes in volume.
 The ratio of force to area $\frac{F}{A}$ is called stress and the ratio of change in length to length $\frac{\Delta L}{L}$ is called the strain.
 Tension: The rod is stretched a length $\Delta L$ when a force is applied parallel to its length.

 In equation form, Hooke's law is given by $F = k \Delta L$ , where $\Delta L$ is the change in length.
 Strain is the change in length divided by the original length of the object.
 Experiments have shown that the change in length (ΔL) depends on only a few variables.
 Additionally, the change in length is proportional to the original length L0 and inversely proportional to the crosssectional area of the wire or rod.
 Tension: The rod is stretched a length ΔL when a force is applied parallel to its length.

 The lensmaker's formula is used to relate the radii of curvature, the thickness, the refractive index, and the focal length of a thick lens.
 The focal length of a thick lens in air can be calculated from the lensmaker's equation:
 The focal length f is positive for converging lenses, and negative for diverging lenses.
 The reciprocal of the focal length, 1/f, is the optical of the lens.
 If the focal length is in meters, this gives the optical power in diopters (inverse meters).

 The simplest case is where lenses are placed in contact: if the lenses of focal lengths f1 and f2 are "thin", the combined focal length f of the lenses is given by
 If two thin lenses are separated in air by some distance d (where d is smaller than the focal length of the first lens), the focal length for the combined system is given by
 If the separation distance is equal to the sum of the focal lengths (d = f1+f2), the combined focal length and BFL are infinite.
 The magnification can be found by dividing the focal length of the objective lens by the focal length of the eyepiece.
 Calculate focal length for a compound lens from the focal lengths of simple lenses

 We define the rotation angle$\Delta \theta$ to be the ratio of the arc length to the radius of curvature:
 The arc length Δs is the distance traveled along a circular path. r is the radius of curvature of the circular path.
 We know that for one complete revolution, the arc length is the circumference of a circle of radius r.
 The arc length Δs is described on the circumference.

 This results in a new vector arrow pointing in the same direction as the old one but with a longer or shorter length.
 A unit vector is a vector with a length or magnitude of one.
 This can be seen by taking all the possible vectors of length one at all the possible angles in this coordinate system and placing them on the coordinates.
 (i) Multiplying the vector A by 0.5 halves its length.
 (ii) Multiplying the vector A by 3 triples its length.