Practice question

**Two lenses in contact** behave as single lens with power sum, magnification product m = m₁×m₂. For f₁=20 cm (P₁=5 D), f₂=-20 cm (P₂=-5 D) in contact, P=0, F infinite, afocal system, beam emerges parallel, principle of corrective lenses for myopia/hypermetropia. Focal length: f = -30 cm (concave lens). Image distance: v = -15 cm (virtual image). Lens formula: (1/v) - (1/u) = (1/f) . (1/-15) - (1/u) = (1/-30) ⇒ (1/u) = (1/-15) - (1/-30) = (-2 + 1/30) = (-1/30) . u = -30 cm . Substituting values gives 30 cm, which matches expected image position and magnification from mirror/lens formula 1/f =