Question

Two identical glass $({\mu }_g=3/2)$ equiconvex lenses of focal length $f$ are kept in contact. The space between the two lenses is filled with water $({\mu }_w=4/3)$. The focal length of the combination is

• A. $f$
• B. $\frac{f}{2}$
• C. $\frac{4f}{3}$
• D. $\frac{3f}{4}$

Answer 1

The correct option is D $\frac{3f}{4}$

Water in between the lenses can be considered to be a concave lens with the refractive index of water as shown in the figure. This suggests that the radius of curvature of all the lenses is same.

For the convex lenses,
$\frac{1}{f}=\frac{({\mu }_g-1)2}{R}=\frac{(\frac{3}{2}-1)2}{R}$

Hence, $R=f$

For the concave lens,

$\frac{1}{f^{\prime }}=({\mu }_{\text{water}}-1)\left(\frac{-2}{R}\right)=\frac{-2}{3f}$

Power of the lenses get added,
$\frac{1}{f_{\text{combination}}}=\frac{1}{f}+\frac{1}{f^{\prime }}+\frac{1}{f}$
$\frac{1}{f_{\text{combination}}}=\frac{1}{f}+\frac{-2}{3f}+\frac{1}{f}$

Hence, $f_{\text{combination}}=\frac{3f}{4}$