In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof.

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## What is center of curvature Class 10?

The centre of curvature is the centre of the sphere of which the spherical mirror is a part. It is denoted by ‘C’.

## What is radius of curvature for Class 9?

Radius of Curvature: The radius of the sphere of which the mirror forms the part. Represented by “R”. Principal axis: The straight line joining the pole (P) and the centre of curvature. It is normal to the mirror at its pole.

## What is the radius of curvature formula?

Formula for Radius of Curvature R = ( 1 + ( d y d x ) 2 ) 3 / 2 | d 2 y d x | In polar coordinates r=r(Θ), the radius of curvature is given by. ρ = 1 K [ r 2 + ( d r d θ ) 2 ] 3 / 2 | r 2 + 2 ( d r d θ ) 2 − r d 2 r d θ 2 |

## What is radius of curvature in short answer?

The radius of curvature is the radius of hollow sphere of which the mirror/spherical mirror is a part of. Solve any question of Ray Optics and Optical Instrument with:- Patterns of problems.

## What is principal axis and radius of curvature?

Radius of curvature – It is the radius of the hollow sphere of which the mirror is a part. It is represented by R. Principal axis – It is a straight line joining the pole of the mirror to its centre of curvature and extended further.

## What is radius of curvature and centre of curvature?

Centre of curvature : The centre of the spherical shell from which the mirror is made, is called the centre of curvature. Radius of curvature : The radius of the spherical shell from which the mirror is made, is called the radius of curvature.

## What is radius of curvature in spherical mirror?

(a) Radius of curvature of a spherical mirror is defined as the radius of an imaginary hollow sphere of which the mirror is a part of. (b) Focal length of spherical mirror is the distance of the point from pole at which all the parallel rays are converged after reflection.

## What is focal length class 10?

The distance between the focus and the optical center is known as focal length. It is denoted by f. Focal length is equal to half the radius of the curvature i.e. f=r/2.

## What is focal length class 10 Ncert?

The focal length of a convex mirror is the distance between the fixation and the convex mirror’s pole. By placing a convex lens between the object and the convex mirror, the focal length of the convex mirror can be calculated.

## What is principal focus Class 10?

When the incident rays are parallel to the principal axis, they converge at a point after refraction. This point where the parallel set of incident rays meet at a point after refraction is called the principal focus of a convex lens.

## What is the formula for curvature?

x = R cost, y = R sin t, then k = 1/R, i.e., the (constant) reciprocal of the radius. In this case the curvature is positive because the tangent to the curve is rotating in a counterclockwise direction. In general the curvature will vary as one moves along the curve.

## What is curvature of a curve?

The curvature of a curve is, roughly speaking, the rate at which that curve is turning. Since the tangent line or the velocity vector shows the direction of the curve, this means that the curvature is, roughly, the rate at which the tangent line or velocity vector is turning.

## What is the radius of 1 degree curve?

If the chord definition is used, each 100-unit chord length will sweep 1 degree with a radius of 5729.651 units, and the chord of the whole curve will be slightly shorter than 600 units.

## What is the relation between R and F?

The relation between focal length (f) and radius of curvature (R) of a spherical mirror is that the focal length is equal to half of the radius of curvature i.e. f=R2.

## What is called centre of curvature?

Definition of center of curvature : the center of the circle whose center lies on the concave side of a curve on the normal to a given point of the curve and whose radius is equal to the radius of curvature at that point.

## What is principal axis class 10th?

The straight line passing through the pole and the center of curvature of the spherical mirror is called the principal axis of a spherical mirror.

## What is called principal axis?

The principal axis is a straight line that passes through the pole and centre of curvature of a spherical mirror.

## What is pole and centre of curvature?

Pole: The centre of reflecting surface. It is represented by letter P.Centre of Curvature: The centre of the sphere of which the mirror forms the part. Represented by “C”.Radius of Curvature: The radius of the sphere of which the mirror forms the part.

## What is the relation between focal length and radius of curvature?

Radius of curvature is observed to be equal to twice the focal length for spherical mirrors with small apertures. Hence R = 2f .

## What is the centre of mirror is called?

The centre of the reflecting surface of a spherical mirror is a point called the pole. It lies on the surface of the spherical mirror.

## What is radius of a concave mirror?

⇒ the length of the concave mirror is K/6 unit. ⇒ Radius of Curvature (R) = 2f ⇒ R = 2*(-K/6) or R = -K/3 unit. Therefore the Radius of Curvature (R) of Concave Mirror is K/3 unit.

## What is radius of curvature of concave lens?

The “radius of curvature” of a concave lens is the distance between the centre of curvature (C ) and the curvature of sphere. There are two radii of curvature for a concave lens, as below.

## What is centre of curvature of mirror?

Centre of curvature of a spherical mirror is defined as the centre of the sphere of which the spherical mirror is a part. In other words, it is the centre of the sphere from which the spherical mirror is sliced.

## What is focal length convex?

The distance between the lens and its focus is known as the focal length of a lens. The focal length of the convex lens is the measure of how sharply it converges the light. For convex lens or converging lens the focal length is always positive. It is denoted by f.