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This involves the rate of change of the unit tangent vector. Deriving the curvature starts with the equation of a circle. Then three equations that force the collocation circle to go through the three points and on the curve must be written down. Then solve for a, b, and r.
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What is mean by centre of curvature?
This means the vented of a circle. It is the radius of the circle that is perpendicular to a line tangent to any point on the concave side of a smooth curve.
What is the difference between the measure of an arc and arc length?
They are normally the same. However, the measure of the arc could refer to the angle subtended at the centre of the radius of curvature.
What does curvature ratio mean in tubing?
Radius of curvature divided by tube diameter. To get the radius of curvature, imaging the bend in the tube is a segment of a circle, the radius of curvature is the radius of that circle.
What is curvature in differential geometry?
There are two most important types of curvature: extrinsic curvature and intrinsic curvature. The extrinsic curvature of curves in two- and three-space was the first type of curvature to be studied historically, culminating in the Frenet formulas, which describe a space curve entirely in terms of its "curvature," torsion, and the initial starting point and direction. There is also a curvature of surfaces in three-space. The main curvatures that emerged from this scrutiny are the mean curvature, Gaussian curvature, and the shape operator. I advice to read the following article: http://mathworld.wolfram.com/Curvature.html Moreover, I advise add-on for Mathematica CAS, which do calculations in differential geometry. http://digi-area.com/Mathematica/atlas There is a tutorial about the invariants including curvature which calculates for curves and surfaces. http://digi-area.com/Mathematica/atlas/ref/Invariants.php
How can find the radius of curvature?
There is a specific formula for finding the radius of a curvature, used often when one is measuring a mirror. The formula is: Radius of curvature = R =2*focal length.
What is definition of centre of curvature of lens?
define the term centre of curvature
What is the ratio of focal length of a spherical mirror to its radius curvature?
The focal point of a convex mirror lies on the same side as the centre of curvature and is at a distance of half the radius of curvature from the optical centre.
Where will the image form when you place an object on the principal axis of a concave mirror at a point between focus and centre of curvature?
The image will form behind the mirror, between the focus and the center of curvature, and it will be a virtual, upright, and magnified image.
How will a ray directed towards the centre of curvature of a convex mirror be reflected?
A ray directed towards the centre of curvature of a convex mirror will reflect back on itself along the same path. This is because the centre of curvature is located on the normal line, so the angle of incidence and the angle of reflection will be equal due to the principle of reflection.
Is the radius In math?
It is the distance, from any point on a curve, to the centre of curvature at that point.
What is the difference between Radius of curvature and centre of curvature?
The radius of curvature is the distance from the center of a curved surface or lens to a point on the surface, while the center of curvature is the point at the center of the sphere of which the curved surface is a part. In other words, the radius of curvature is the length of the line segment from the center to the surface, while the center of curvature is the actual point.
What is the center of curvature of the mirror?
The center of curvature of a mirror is the point located at a distance equal to the radius of curvature from the mirror's vertex. It is the center of the sphere of which the mirror forms a part. Light rays that are reflected from the mirror and pass through this point are either parallel to the principal axis (for concave mirrors) or appear to diverge from this point (for convex mirrors).
A line joining pole and centre of curvature of the mirror is called?
The line joining the pole and the centre of curvature of a mirror is called the principal axis. This line is a key reference point for determining the focal length and characteristics of the mirror.
What is mathimatical radious?
In mathematics, the radius of an arc is a straight line from the centre of curvature of the arc to the arc. In the case of a circle it is the line from the circle's centre to its circumference.
What is the exact relation of the focal length to the center of curvature?
The focal length (a.k.a focus) is exactly half the length of the centre of curvature. ie. F = 1/2 C
An object is placed between focus and centre of curvature of a concave mirror. Draw a ray diagram and derive mirror formula. Also write magnification formula.?
In a concave mirror, when an object is placed between the focus and the center of curvature, the image formed is real, inverted, and enlarged. To derive the mirror formula, use the mirror formula: 1/f = 1/v + 1/u, where f is the focal length, v is the image distance, and u is the object distance. The magnification formula is: M = -v/u, where M is the magnification, v is the image distance, and u is the object distance.
What is definition for the centre of curvature of a spherical mirror?
The center of curvature of a spherical mirror is the point at the center of the sphere from which the mirror is a part. It is located at a distance equal to the radius of the sphere. The center of curvature is an important point for determining the focal length and the magnification of the mirror.
