Question

What is the relation between focal length and radius of curvature of a concave mirror? Does the same relation hold for a covcave mirror?

Answer 1

Relation between the focal length and radius of curvature :

For a spherical mirror of small aperture to its radius of curvature, the focal length of the mirror is one half of the radius of curvature of the mirror.

This relation can be proved for both the mirrors that is concave and convex.

$f = \frac{1}{2}r$

here f is the focal length and r is the radius of curvature..

Yes, both the lens holds the same relation..

In the given attachment : derivation for both the mirror ( convex and concave)

Answer 2

$\huge\bold\green{Question}$

What is the relation between focal length and radius of curvature of a concave mirror? Does the same relation hold for a covcave mirror?

$\huge\bold\green{Answer}$

As we know that mirror formula is :-

$\large \sf \implies \blue{ \: \frac{1}{v} + \frac{1}{u} = \frac{1}{f} } \:$

And , we also know that :-

$\sf \implies \blue{radius \: of \: curvature = 2(focal \: length}$

So, let “ R ” is the radius of curvature than :-

$\sf \implies \blue{ f = \frac{R}{2} } \:$

Now , use this formula in mirror formula :-

$\sf \implies \blue{ \frac{1}{v} + \frac{1}{u} = \frac{2}{R} }$

This relation can be proved that for both the mirrors concave and convex can be :-

$\sf\implies \blue{f = \frac{1}{2} r}$

•°• f = focal length

•°• r = radius of curvature

So , we can conclude that both the lens holds the same relation.