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Question

A converging beam meets a convex lens (\( f = 12 \, \text{cm} \)) \( 6 \, \text{cm} \) before the
convergence point. What is the new image 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. Object distance: u = -6 cm (virtual object), f = 12 cm . Lens formula: (1/v) - (1/-6) = (1/12) ⇒ (1/v) + (1/6) = (1/12) . (1/v) = (1/12) - (1/6) = (1 - 2/12) = (-1/12) . v = -12 cm (12 cm to the left).

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