A beam of convergent light converges to a point 0.5 m in front of the mirror after reflection at a convex mirror but in the absence of the mirror the beam converges to a point 0.2 m behind the mirror. The radius of curvature of the mirror is :-

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Using the mirror formula with sign conventions:

$\frac{1}{v} + \frac{1}{u} = \frac{2}{R}$

Given: $v = - 0.5$ m (real image), $u = + 0.2$ m (virtual object). Substituting these values:

$\frac{1}{- 0.5} + \frac{1}{0.2} = \frac{2}{R}$

$- 2 + 5 = \frac{2}{R}$

$3 = \frac{2}{R}$

$R = \frac{2}{3} \approx 0.667 m = 66.67 c m$

Therefore, the radius of curvature of the mirror is approximately 66.67 cm.

Physics - Geometrical Optics Question with Solution | TestHub

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