A convex lens of focal length 10 cm is combined with a concave lens of focal length 6 cm. Find the focal length of the combination.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −15 cm
For thin lenses in contact the powers add, \( 1/F=1/f_1+1/f_2 \). With the Cartesian sign convention the convex lens has \( f_1=+10\,\mathrm{cm} \) and the concave lens \( f_2=-6\,\mathrm{cm} \).
\( \begin{aligned} \frac{1}{F} &= \frac{1}{+10\,\mathrm{cm}}+\frac{1}{-6\,\mathrm{cm}} \\ &= \frac{3-5}{30\,\mathrm{cm}} \\ &= -\frac{1}{15\,\mathrm{cm}} \end{aligned} \)
\( F=-15\,\mathrm{cm} \)
The negative sign means the combination behaves as a diverging (concave) lens.