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Pole: It is the geometrical centre of the reflecting surface. It is represented by the letter P. Centre of curvature: It is the centre of the sphere of which the mirror forms the part. It is represented by C. The radius of curvature: It is the radius of the sphere of which the mirror forms
In geometry, the center of curvature of a curve is found at a point that is at a distance from the curve equal to the radius of curvature lying on the normal vector. It is the point at infinity if the curvature is zero.
Feb 27, 2022 · The centre of the circle of curvature is called centre of curvature at the point. These definitions are illustrated in the figure below. It shows (part of) the osculating circle at the point \(P\text{.}\)
Centre of Curvature Incidence: A ray passing through the centre of curvature of a spherical mirror will retrace its path after reflection. This principle illustrates that when a ray hits the mirror’s centre of curvature, it undergoes reflection and follows the exact same path in the opposite direction.
Mar 10, 2022 · Finally the centre of curvature is \[\begin{align*} \vecs{r} (t) +\frac{1}{\kappa(t)}\hat{\textbf{N}}(t) &=\Big(a-\frac{a^2+b^2}{a}\Big)\cos t\,\hat{\pmb{\imath}} +\Big(a-\frac{a^2+b^2}{a}\Big)\sin t\,\hat{\pmb{\imath}} +bt\,\hat{\mathbf{k}}\\ &=-\frac{b^2}{a}\cos t\,\hat{\pmb{\imath}} -\frac{b^2}{a}\sin t\,\hat{\pmb{\imath}} +bt\,\hat{\mathbf ...
Jul 25, 2021 · Before learning what curvature of a curve is and how to find the value of that curvature, we must first learn about unit tangent vector. As the name suggests, unit tangent vectors are unit vectors (vectors with length of 1) that are tangent to the curve at certain points.
The centre of the circle of curvature is called centre of curvature at the point. These definitions are illustrated in the figure below. It shows (part of) the osculating circle at the point \(P\text{.}\)
