Practice question

**Combination of lenses in contact** effective power P = P₁+P₂, effective focal length 1/F = 1/f₁ + 1/f₂, for thin lenses in contact. If separated by d, 1/F =1/f₁+1/f₂ - d/(f₁ f₂). Power adds algebraically, converging + with diverging - can cancel, used to correct aberrations and design achromatic doublets. Focal length: f = 30 cm , u = -15 cm . Mirror equation: (1/v) + (1/-15) = (1/30) ⇒ (1/v) = (1/30) + (1/15) = (1 + 2/30) = (3/30) = (1/10) . v = 10 cm . Magnification: m = -(v/u) = -(10/-15) = 0.67 . Substituting values gives 0.67, which matches expected