Two identical equiconvex glass lenses, each of focal length f, are kept in contact. The space between them is filled with water, which forms a concave (diverging) lens of focal length of magnitude \( 3f/2 \). The focal length of the combination is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 3f/4 \)
The water between the glass lenses acts as a third lens, so the system is three thin lenses in contact. Their powers add, so \( 1/F=1/f_1+1/f_2+1/f_3 \). Each glass lens has focal length \( +f \), and the diverging water lens has \( -3f/2 \).
\( \begin{aligned} \frac{1}{F} &= \frac{1}{f}+\frac{1}{f}+\frac{1}{-3f/2} \\ &= \frac{2}{f}-\frac{2}{3f} \\ &= \frac{4}{3f} \end{aligned} \)
\( F=3f/4 \)
The positive sign means the combination is converging.