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Give The formula for radius of curvature in polar form?
The radius of curvature is given by(1)where is the curvature. At a given point on a curve, is the radius of the osculating circle. The symbol is sometimes used instead of to denote the radius of curvature (e.g., Lawrence 1972, p. 4).Let and be given parametrically by(2) (3)then(4)where and . Similarly, if the curve is written in the form , then the radius of curvature is given by
How do you find the radius given the chord length?
If you are given a chord length of a circle, unless you are given more information about the chord, you can not determine what the radius of the circle will be. This is because the chord length in a circle can vary from a length of (essentially) 0, up to a length of double the radius (the diameter). The best you can say about the radius if given the chord length, is that the length of the radius is at least as long has half half the chord length.
How do you find the central angle of a circle if I am given the arc length and radius?
(arc length / (radius * 2 * pi)) * 360 = angle
How do you find radius of curvature in achromatic lens if focal length and diameter is given?
You also need to know the index of refraction. For glass, that is usually somewhere around 1.5. The Wikipedia article on "Lens (optics)" includes the "Lensmaker's equation"; usually you can use the "thin lens equation" (further down in the article) as a convenient approximation. Since for this question you don't know the radius of curvature, and the equation includes two radii of curvature (for the two surfaces), I suggest that you make one of the following simplifying assumptions: 1) Either assume that the lens has two surfaces of equal curvature (note: for the equation in the Wikipedia article, the signs would be opposite for both sides), 2) Or, assume that the lens has one flat side and one curved side.
What is the locus of the midpoints of all chords of length 4 in a given circle with radius of length 3?
Looks to us like it's another circle, concentric with the first one, with radius of sqrt(5) = 2.236 . (rounded)
