Combination Of Lenses

Two thin lenses in contact behave as one lens whose power is the algebraic sum of the individual powers, since powers add directly: $P=P_1+P_2$. The converging lens contributes $+5$ D and the diverging lens contributes $-2$ D, so $P=5+(-2)=+3$ D. The equivalent focal length follows from $f=\frac{1}{P}$ with $P$ in dioptre and $f$ in metres, giving $f=\frac{1}{3}=0.333$ m $=33.3$ cm. The positive result shows the combination still converges overall. Powers add so cleanly only because the lenses are in contact, making the separation negligible; the rays leaving the first lens strike the second before they have spread or converged appreciably, so each lens deflects them in turn and the deflections superpose. Expressing lenses by power rather than focal length turns this superposition into simple addition, which is why opticians prescribe corrective lenses in dioptres. The value 50 cm is wrong because it would require a net power of 2 D, ignoring the converging lens's larger contribution. The value 14.3 cm corresponds to a net 7 D, which mistakenly adds magnitudes instead of respecting the negative sign. The value 20 cm matches 5 D alone, neglecting the second lens. This is the NCERT rule for lenses in contact used in achromatic doublets. A check confirms the weaker diverging lens reduces but does not reverse the net convergence.