Practice question

**Lens combination** effective focal length calculation uses reciprocal sum, for f₁=10 cm, f₂=20 cm in contact, 1/F=1/10+1/20=3/20, F=6.67 cm, P=15 D, stronger converging than either alone, illustrating power addition. Focal length: f = 24 cm (convex mirror). Image distance: v = 8 cm (virtual image). Mirror equation: (1/v) + (1/u) = (1/f) . (1/8) + (1/u) = (1/24) ⇒ (1/u) = (1/24) - (1/8) = (1 - 3/24) = (-2/24) = (-1/12) . u = -12 cm . Substituting values gives 10 cm, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f = 1/v + 1/u