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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 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.
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
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)
Can focal length and radius of curvature of a lens be same?
No, the focal length and radius of curvature of a lens cannot be the same. The radius of curvature is twice the focal length for a lens. This relationship is based on the geometry of the lens and the way light rays converge or diverge when passing through it.
What was the focal length when the radius of curvature was 0.70 m and index of refraction was 1.8?
The focal length of a lens is related to its radius of curvature and the index of refraction by the lensmaker's equation: [\frac{1}{f} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)] Given the radius of curvature (R = 0.70 , m) and the index of refraction (n = 1.8), you can calculate the focal length.
Formula of radius of curvature of double convex lens?
The formula for the radius of curvature (R) of a double convex lens is given by R = 2f, where f is the focal length of the lens. The radius of curvature is the distance from the center of the lens to the center of curvature of one of its curved surfaces.
Why is the focal length of a plane mirror infinity?
In a plane mirror, the radius of curvature is infinitly long, so the focus will be at infinity. Another way to say it is that a plane mirror has no curvature, and as curvature becomes increasingly small, focal length becomes increasingly long. At a curvature of zero, focal length becomes infinite. Focal length(f) is given by f=R/2 where R is radius of curvature.. Once again, it's infinity! See answer to your question on radius of curvature. Plug infinity (radius of curvature) into your mirror equation to get the focal length, which will also be infinite. A flat mirror does not focus incoming parallel beams. That's because if you say its at infinity it means it does exist in a finite distance, that is instead of saying it does exist its taken at infinite distance for only theoretical importance and not for practical observance. Focal length is half of radius of curvature of the mirror. So bigger the circle gets the more its radius will be. So in the same way as the curvature of the sphere gets less and less its focal length increases, so when it becomes totally flat the focal length will become infinite so it means it has no existence but it has only theoretical importance. It same as taking the formation of image of an object at principal focus to be at infinite distance rather than saying it does not form ( that is both mean the same). hope my answer is satisfactory
If a telescope has an objective lens of 3 inches what is the focal length?
The focal length of a telescope is dependent on the design and specifications. It cannot be determined solely based on the objective lens size. The focal length needs to be provided by the manufacturer or measured using specific techniques.
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
What is the radius of curvature?
The radius of curvature of a circle, or an arc of a circle is the same as the radius of the circle.For a curve (other than a circle) the radius of curvature at a given point is obtained by finding a circular arc that best fits the curve around that point. The radius of that arc is the radius of curvature for the curve at that point.The radius of curvature for a straight line is infinite.
What is the formula for figuring curvature of the earth in any given direction?
The curvature of the Earth in any direction can be calculated using the formula for the Earth's radius of curvature (R), which is given by R = a / β(1 - e^2sinΒ²Ο) where a is the equatorial radius of the Earth and e is the eccentricity of the Earth. By determining the radius of curvature at a specific latitude (Ο), you can find the curvature in that direction.
How do you find radius of curvature if image distance is given?
There is not enough information to answer the question.
Is the focal length of a concave mirror is half the radius of curvature?
As shown in the figure, a paraxial ray is incident at point Q on a concave mirror. q = angle of incidence = angle of reflection = Ð CQF = Ð QCF ( by geometry ) So, for D CFQ, exterior Ð QFP = Ð CQF + Ð QCF = 2q . For paraxial incident ray and small aperture, CP' » CP = R and FP' » FP = f. For small aperture, 2q is very small. \ from the figure, 2q » FP QP = f QP … ( 1 ) and q = CP QP = R QP … ( 2 ) From equations ( 1 ) and ( 2 ), R = 2f ⇒ f = R / 2 Thus, focal length of a concave mirror is half its radius of curvature.
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.
What is a surface normal?
There is no such expression. The normal to a surface, at a given point is the radius of curvature of the surface, at that point.
