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Question

A convex mirror of radius of curvature \( 40 \, \text{cm} \) forms an image \( 10 \, \text{cm} \)
behind the mirror. What is the object distance?

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Explanation

**Mirror formula** 1/f = 1/v + 1/u governs spherical mirrors, f = R/2, R radius of curvature (m), u object distance (m), v image distance (m), sign convention: distances in front of mirror negative for real is convention but magnitude used, magnification m = -v/u, concave forms real inverted when object beyond F, virtual erect within F. Focal length: f = (R/2) = (40/2) = 20 cm (convex mirror). Image distance: v = 10 cm (virtual image). Mirror equation: (1/v) + (1/u) = (1/f) . (1/10) + (1/u) = (1/20) ⇒ (1/u) = (1/20) - (1/10) = (1 - 2/20) = (-1/20) . u =

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