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# Converging rays are incident on a convex spherical mirror so that their extensions intersect $30\,cm$ behind the mirror on the optical axis. The reflected rays form a diverging beam, so that their extensions intersect the optical axis $1.2\,m$ from the mirror. The focal length of the mirror is A. $40\,cm$B. $60\,cm$C. $30\,cm$D. $24\,cm$

Last updated date: 19th Jul 2024
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Hint: Reflected rays get diverged or converged to form an image while incident rays are converged to form an object. Thus image distance and object distance can be obtained from the question and we must find the focal length of the mirror by using the mirror formula in this scenario.

When the reflected rays diverge so that their extensions intersect at a point, then that point is our image and the distance of that image from the center of curvature is called image distance. Object distance is denoted as u and image distance is denoted as $v$.The focal length (f) of the mirror can be obtained from the mirror formula as follows:
$\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$
$\Rightarrow \dfrac{1}{f} = \dfrac{1}{{120}} + \dfrac{1}{{30}}$
$\therefore f = 24\,cm$