Question

Relationship between Radius of Curvature and Focal length..​

Answer 1

$\large{\underline{\underline{\mathbf{Relationship\:Between\:!}}}}$

$\small{\underline{\underline{\mathbf{Radius\:Of\:Curvature\:and\:Focal\:Length\:!!}}}}$

Before arriving at the answer let us first understand the meaning of these terms:-

⭕RADIUS OF CURVATURE:-

✍It is known to us that a spherical mirror has a pole and a point called the "centre of curvature ".

✍This distance between the pole and the centre of curvature is the RADIUS OF CURVATURE.

⭕FOCAL LENGTH:-

✍It is the length between the pole of a spherical mirror (optical centre of lens) and the focal point.

✍It is positive in case of a convex mirror and negative in that of a concave mirror.

▶️Let us now come at the relation between the focal length and centre of curvature.

$focal \: length = \frac{1}{2} (radius \: of \: curvtature)$

⭕One important thing to be noted is that, in case of a plane mirror, the radius of curvature is taken as infinity.

⭕In case of lens ,if you are provided with refractive indices of the medium, you can have the lens maker formula.

$\frac{1}{f} = n - 1( \frac{1}{ r_{1} } - \frac{1}{ r_{2} } )$

where f is the focal length and r1 and r2 are the radius of curvature respectively. ✔✔

Answer 2

Answer:

★ The Radius of Curvature (r) is the radius of the lens that forms a complete sphere.

★ The Focal Length (f) of a lens is the distance between the center of the lens and the point at which the reflected light, of a beam of light travelling parallel to the center line, meets the center line (principal axis).

† Refer to Attachment for more information .