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This starts with the collocation circle to go through the three points on the curve. First write the equation of a circle. Then write three equations that force the collocation circle to go through the three points on the curve. Last, solve the equations for a, b, and r.

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Q: How do you get the formula center of curvature?
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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 a mirror?

A plane mirror is not curved so it does not have a center of curvature. Or if you want to be mathematically correct, you could say that it's center of curvature is at an infinite distance from the mirror.


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.


What is the center of curvature of a lens?

The center of curvature of a lens is the point located at a distance equal to the radius of curvature from the center of the lens. It is the point where the principal axis intersects the spherical surface of the lens.


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 are the parts of concave mirror?

The main parts of a concave mirror are the pole (center point), principal axis (imaginary line passing through the pole and center of curvature), focal point (half the distance between the pole and center of curvature), and the center of curvature (center of the sphere from which the mirror is a section).


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.


Center of curvature in differential calculus?

Center of curvature = r(t) + (1/k)(unit inward Normal) k = curvature Unit inward normal = vector perpendicular to unit tangent r(t) = position vector


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 / √(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.


What is the relation between focal length and center of curvature?

The focal length of a concave mirror is about equal to half of its radius of curvature.


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).


True or false the center of curvature of a plane mirror is at infinity?

False. The center of curvature of a plane mirror is not at infinity, but rather it is located at a point behind the mirror at a distance equal to the radius of curvature.