AB and CD, two spherical mirrors, form parts of a hollow spherical ball with its centre at O as shown in the diagram. If arc $\text{AB}=\frac{1}{2}$ arc CD, what is the ratio of their focal lengths? State which of the two mirrors will always form virtual image of an object placed in front of it and why.
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The ratio of the focal lengths of mirrors AB and CD will be equal to one as both the mirrors are part of same spherical ball. Hence, their radius of curvature and focal length will be same. The mirror AB will always form a virtual image when object is placed infront of it because mirror AB is a conex mirror.
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