Power And Combination Of Lenses

When thin lenses are placed in contact, NCERT shows that their powers add algebraically, so the combined power is $P=P_1+P_2$, where power in dioptres equals the reciprocal of the focal length in metres. Here $P_1=+5$ D for the converging lens and $P_2=-2$ D for the diverging lens, giving $P=5+(-2)=+3$ D. The positive result means the combination behaves as a converging system with an effective focal length of $f=\frac{1}{P}=\frac{1}{3}\approx 0.33$ m. The value $+7$ D is wrong because it adds the magnitudes while ignoring the negative sign of the diverging lens. The value $-3$ D is wrong because it reverses which lens dominates, but the stronger positive power wins. The value $+2.5$ D is wrong because it averages the powers rather than summing them, which is not how contact lenses combine. As stated in NCERT Class 12, Chapter 9, powers add directly only when lenses are in contact with negligible separation. A sign check confirms that a strong converging lens paired with a weaker diverging one still converges overall, matching the positive result.