The radius of curvature of a convex spherical mirror is 1.2 m. How far away from the mirror is an object of height 12 cm If the distance between its virtual image and the mirror is 0.35 m? What is the height of the image ?
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Since radius of curvature is $$1.2\;{\rm{m}}$$ i.e. $$120\;{\rm{cm}}$$.
Therefore focal length$$ = - 60\;{\rm{cm}}$$
From mirror formula
$$\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$$
$$\dfrac{1}{{ - 35}} + \dfrac{1}{u} = \dfrac{1}{{ - 60}}$$
$$\dfrac{1}{u} = \dfrac{1}{{35}} - \dfrac{1}{{60}}$$
$$\dfrac{1}{u} = \dfrac{{12 - 7}}{{420}}$$
$$u = 84\;{\rm{cm}}$$
Image height$$ = \dfrac{{12}}{{84}} \times 35 = 5\;{\rm{cm}}$$
Thus image height will be 5 cm.
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