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Question

A convex mirror of focal length \( 10 \, \text{cm} \) forms an image \( 5 \, \text{cm} \) behind the
mirror. What is the object distance?

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Explanation

**Spherical mirror reflection** follows law θ_i = θ_r, focal length f = R/2, concave R negative, convex positive. Object beyond center C (u > 2f) forms image between F and C diminished, at C same size, between C and F magnified, beyond F forms at infinity, illustrating mirror equation. Focal length: f = 10 cm (convex mirror). Image distance: v = 5 cm (virtual image). Mirror equation: (1/v) + (1/u) = (1/f) . (1/5) + (1/u) = (1/10) ⇒ (1/u) = (1/10) - (1/5) = (1 - 2/10) = (-1/10) . u = -10 cm . Substituting values gives 5 cm, which matches expected image

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