Question

an object is 30cm from a spherical mirror, along the central axis. the absolute value of lateral magnification is 1/2. the image produced is

Answer 1

$\huge\textbf{SOLUTION}$
$<b>$

$\textbf{Object's Distance from a spherical mirror= 30cm}$

$\textbf{Image is inverted , so it is real}$

$\textbf{Also u and v both are negative}$

$\textbf{Magnification is given = 1/2}$

$\boxed{Therefore , v = \frac{u}{2}}$

$\textbf{Given , u = -30 cm and v = -15 cm}$

$\textbf{Using Mirror's formulae we have}$

$\frac{1}{v} = \frac{1}{u} + \frac{1}{f} \\ \\ \frac{1}{f} = \frac{1}{ - 15} - \frac{1}{30} \\ \\ \frac{1}{f} = \frac{ - 1}{10}$

$\textbf{Focal length of mirrors =>10 cm}$

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