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The shiny outer surface of a hollow sphere of aluminium of radius 50 cm is to be used as a mirror:(a) What will be the focal length of this mirror?(b) Which type of spherical mirror will it provide?(c) State whether this spherical mirror will perge or converge light rays.
(a) Given:
The radius of curvature of the mirror, $R$ = 50 cm.
We know that the focal length, $f$ is equal to the half of the radius of curvature, $R$, it is given as:
$f=\frac {1}{2} \times {R}$
Now, putting the value $R$ in the above equation we get-
$f=\frac {1}{2} \times {50}$
$f=25cm$
Hence, the focal length of this mirror will be 25 cm.
(b) Since the outer surface is shiny, it will provide a convex mirror.
(c) This spherical mirror will diverge the light rays.
Explanation
If a spherical mirror, containing the inner surface shiny or polished, then it will be a concave mirror, whereas a spherical mirror, containing the outer surface shiny or polished, then it will be a convex mirror.
A concave mirror converges the light rays due to which it is also known as a converging mirror, whereas a convex mirror diverges the light rays, and also known as a diverging mirror.
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