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. Refractive index: n = (sin ( (A + D_m/2) )/sin ( (A/2) )) . A = 60° , D_m = 36° . n = (sin ( (60 + 36/2) )/sin ( (60/2) )) = (sin 48°/sin 30°) . sin 48° ≈ 0.743 , sin 30° = 0.5 . n = (0.743/0.5) ≈ 1.486 . Substituting values gives 1.49, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f